maths problem solving grade 4

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4th Grade Math Worksheets

Endorsing learning and practice, our printable 4th grade math worksheets with answer keys amazingly fit into your curriculum. With adequate exercises in multi-digit multiplication, and division, equivalent fractions, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers, analyzing and classifying geometric figures based on their properties, such as parallel and perpendicular sides, angle measures, and symmetry, converting between units of measurement, making and interpreting line plots, these pdfs become the most sought after. Grab our free grade 4 math worksheets for a peek into what's in store.

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Explore 5,600+ Fourth Grade Math Worksheets

Adding 4-Digit Numbers

Repetition is the surefire way to swiftly and accurately add up two 4-digit numbers. Fuel practice in regrouping in the ones, tens, hundreds, and thousands place in the process.

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Multiplication for Beginners | Factors Up to 12

If buffing up multiplication skill is on your mind, then our 4th grade math worksheet pdfs should be an obvious choice. Find the product of numbers up to 12 and solve real-life word problems too.

Listing out the Factors | Easy (1 to 50)

Break down each number into its components by finding the factors that when multiplied result in the given number. List out all the possible factors of each specified number from the least to the greatest.

Completing the Shape Pattern

Develop skills in pattern analysis with our printable math worksheets. Grade 4 kids observe the repeating pattern in each set of shapes, predict and draw the missing shape in each series.

Writing Number Words | Millions

Translate the 7, 8, and 9-digit numerals to the number words: millions, ten millions, and a hundred millions, as you work your way doubling up and enhancing your place value skills.

Writing the Missing Numbers in Equivalent Fractions

The numerator and denominator of a fraction must be multiplied or divided by the same number to create equivalent fractions. Apply this rule to figure out the missing numbers in these 4th grade math pdfs.

Measuring and Converting Inches to Feet and Inches

Build a vital life-skill as you practice measuring the length of the strips of paper in inches using the given ruler, and divide the length by 12 to express the measurement in feet and inches.

Interpreting Line Plots

Draw conclusions by interpreting the data organized as line plots in our printable grade 4 math worksheets and calculate the mean, median, mode and range to answer questions based on the line plot.

Identifying Points, Lines, Rays, and Line Segments

Look at the arrowheads and dots, and recognize each model as a point, line, ray, or line segment in Part A. Attempt sketching a line, ray, and line segment in Part B.

Parts of an Angle | Naming the Vertex and Arms

Get the know-it-alls of 4th grade to identify the parts of an angle: arms, the two rays joining to form an angle, and the vertex which is the common end point and name them in these math worksheet pdfs.

Classifying Triangles using Side Measures

How about classifying triangles based on their side measures? Label the triangles with three equal sides as equilateral, and those with two equal sides as isosceles, and the ones with unequal sides as scalene.

Drawing Lines of Symmetry | Shapes

Gravitate toward our printable 4th grade math worksheets to practice drawing a line across the shape dividing it into two identical halves and identifying if the figures are horizontally or vertically symmetrical.

Solving Multi-Digit Addition Word Problems

Armed with a touch of real-world, our exercises inculcate a love for math in grade 4 kids as they solve word problems, working with 4 to 8-digit addends, and figure out the sum.

Multiplication Drill | 50 Problems

Nothing promotes multiplication recapitulation quite like these 4th grade math worksheet pdfs. Beat the clock as you work out the timed multiplication drill comprising 50 problems each.

Finding Factors | Prime and Composite

Step up your practice in finding the factors of the numbers and identifying if the specified number is prime (divisible only by the number 1 or by itself) or composite.

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Grade 4 Word Problem Worksheets

Free printable fourth grade math worksheets to help your students improve their ability to solve word problems! Applying mathematical concepts to solve word problems can be challenging. These free worksheets are great repetition for your students! Click on the images below to download the word problem worksheets. They’re perfect for daily math warm ups! Don’t forget to check out the word problem task cards. Print them off, laminate them and use them for early finishers during maths!

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Problem Solving

Problem solving is an essential skill in math, and in everyday life. It involves identifying a problem, analyzing it, and finding a solution. To become a successful problem solver, you need to understand the different strategies and techniques that can be used to approach and solve problems.

Steps for Problem Solving:

• Understand the Problem: Read the problem carefully, and make sure you understand what it is asking. Identify the key information and what you are trying to find.
• Make a Plan: Decide on a strategy to solve the problem. You can use strategies like drawing a picture, making a table, working backward, or using logical reasoning.
• Carry Out the Plan: Use the strategy you selected to solve the problem. Perform the necessary calculations and operations to find the solution.
• Check the Solution: After finding a solution, review your work to ensure that it makes sense and answers the original problem.

Problem Solving Strategies:

There are various problem solving strategies that can be used to tackle different types of problems. Some common strategies include:

• Guess and Check: Guessing a solution and checking to see if it works.
• Draw a Picture: Visualizing the problem by drawing a diagram or picture.
• Make a Table: Organizing data in a table to look for patterns or relationships.
• Work Backward: Starting with the end goal and working backward to find the steps needed to reach that goal.
• Use Logical Reasoning: Applying logical thinking to analyze and solve the problem.

Practice Problems:

To become proficient at problem solving, it's important to practice solving a variety of problems. Here are a few practice problems to get you started:

• Sarah has 5 apples. She gives 2 apples to her friend. How many apples does she have left?
• If a book has 350 pages and Tom reads 50 pages each day , how many days will it take him to finish the book?
• Alice is twice as old as Bob. If Alice is 20 years old, how old is Bob?

By practicing problem solving regularly, you can improve your skills and become a more confident and successful problem solver!

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Check Out These 50 Fourth Grade Math Word Problems of the Day

Mr. Smith’s class collected coins in a big jar for 6 months.

Opening your daily math lesson with a Fourth Grade Math Word Problem of the Day is an excellent way to set the stage for learning! Incorporate them at the start of your math block to build confidence, critical thinking skills, and a learning community. Students will get used to reading for meaning, while also identifying key information. Encourage students to write out equations and draw pictures to explain their thinking, since this helps them see the light when they are stuck!

Topics in these fourth grade math word problems cover patterns & place value, addition/subtraction, multiplication, division, fractions, decimals, measurement, and comparisons. If you’d like even more math word problems, we publish them daily on our kid-friendly site: the Daily Classroom Hub . Make sure to bookmark the link!

Want this entire set of word problems in one easy document? Get your free PowerPoint bundle by submitting your email here . All you need to do is post one of the problems on your whiteboard or projector screen. Then let kids take it from there.

50 Fourth Grade Math Word Problems

1. jill wrote the number 730,918. she challenged jane to rearrange the digits to create the highest possible number. what number did jane make.

2. Marcus was given this puzzling pattern and asked to complete it. Which two numbers should he should write next? 4, 7, 11, 14, 18, 21, 25, ___, ___

3. Mr. Mathematica gave his class these digits: 1, 5, 7, 9, 2, 8, and 5. He asked them to make the smallest number possible using every digit once. What would that number be?

4. The detectives found this number pattern as part of the code on a keypad to unlock a vault. 27, 26, 24, 23, 21, __, __. What are the last two numbers they should punch in?

5. Tom’s bicycle cost $50 more than Bob’s bicycle. Bob’s bicycle cost $180. How much did Tom’s bicycle cost?

6. Randy bought 2 baseball hats for $5.25 each. He also bought 2 wrist bands for $2.50 each. How much money did he spend?

7. Lots of birds were spotted at the new bird feeder. There were 12 sparrows, 15 crows, 8 orioles, 3 squirrels, and 9 cardinals. How many birds were there in all?

8. There were lots of visitors to the town history museum this past winter. There were 75 in December, 98 in January, and 69 in February. How many visitors did the museum have this past winter in total?

9. Luis was setting up his new office. He bought a new computer for $350. He also bought a printer for $99 and two ink cartridges for $37 each. How much did he spend?

10. There was a big sale at the Super Duper Shoe Store for 3 days. They sold 87 pairs of shoes on Friday, 95 pairs of shoes on Saturday, and 83 pairs of shoes on Sunday. How many pairs of shoes were sold all together?

11. Pia had a huge sticker collection. She had 280 stickers. Her friend, Jen, had 155 stickers in her collection. How many more stickers did Pia have than Jen?

12. Robyn scored a total of 155 points in basketball this season for the Tarrytown Tigers. She had 30 rebounds as well. Last season she scored 106 points. How many more points did she score this season than last season?

13. John went to lunch at the Cool Cat Cafe. He spent $1.25 on a juice drink and $5.50 on a sandwich. He also bought a brownie for 99 cents. He gave the cashier a $20 bill. How much change did he get?

14. Race Car Ralph drove 1,000 miles in the big cross-country auto race. 775 of those miles were with his dog, Speedy, in the car. The rest of the way, he drove alone. How many miles did Ralph drive without Speedy?

15. Best Baked Bakery baked 10,250 holiday cookies. They sold almost all of them. Only 56 were left. How many holiday cookies did they sell?

16. There were 3 cats and 4 geese in the barnyard. How many total legs were there?

17. Donna picks 5 apples every minute in the orchard. How many apples does she pick in 20 minutes?

18. Morris the magician pulled 2 doves out of his hat, twice as many rabbits as doves, and 4 times as many mice as rabbits. How many animals did he pull out of his hat?

19. Tina is making pizzas for 15 guests. If each person (including Tina) is expected to eat 2 slices, how many 8-slice pizzas should Tina make?

20. Chef Charlie is decorating a birthday cake with a circle of berries. He has 6 strawberries and would like to put 5 blueberries between each strawberry. How many blueberries does he need?

22. To make a winter stew, Jamal needs 3 pounds of sweet potatoes. If they cost $1.29 per pound, what will it cost to buy enough sweet potatoes?

22. The Hotel Swanky has 10 floors. Each floor has 16 guest rooms. There is also a ballroom, two meeting rooms, and a restaurant. How many guest rooms are in the hotel?

23. Mrs. Mason got a new bookcase for the library and filled it with books. There were 6 shelves. The top two shelves had 50 books on each shelf. The bottom four shelves had 75 books on each shelf. How many books were there in the new bookcase?

24. The cafeteria ordered 6 packs of jumbo chocolate chip cookies and 3 packs of brownies. Each pack of cookies had 12 cookies in it. They sold 45 cookies and 30 brownies. How many cookies are left?

25. The new elementary school has 30 desks in each classroom. There are four classrooms for each grade. There are 5 grades in the school. How many desks are there in the school?

26. Gina planted six rows of carrots in her garden. Each row had 30 carrots. Rabbits ate half of her carrots. How many carrots did she have left?

27. Jack planted a magic bean. The bean plant that grew was 1 foot tall on the first day. Then it doubled in height each day. How tall was the plant on the fifth day?

28. Big Brain University bought 15 new supercomputers and 50 printers. Each supercomputer cost $5,300. A printer cost $100. How much did the university spend buying new computers?

29. The new golf course had 3 tournaments every month this year. The course is open 12 months a year. Each tournament was limited to 101 golfers and was full. How many golfers played in the tournaments all together this year?

30. The school office printer can print 200 pages every 10 minutes. If the printer runs for an hour straight, how many pages can it print?

31. Lucia makes beaded bracelets. Each bracelet has 12 beads on it. She made 55 bracelets for each of the school fairs. The school had 3 fairs. How many bracelets did Lucia make?

32. Sammy Speedball is a pitcher for the Boogaloo Bearcats. He practiced his pitching on Saturday for an hour in the morning and an hour after dinner. He threw 20 pitches every 30 minutes. How many practice pitches did Sammy throw on Saturday?

33. Serena had 35 cherries. She gave 8 to each of her sisters. She still has 3 left over. How many sisters does Serena have?

34. The new teacher was giving out pencils to her class for the year. She wanted to give them out evenly. She had 15 packs of pencils with 10 pencils in each pack. She had 20 students. How many pencils should each student get? How many pencils would be left over?

35. 150 kids signed up for the summer soccer league. There are going to be ten teams, and the Dragons are one of the teams. Each team has 3 coaches and they want an equal number of players on each team. How many players should be on the Dragons?

36. the wonderful widget company produces 480 widgets every day. they have 6 widget making machines running every day, with each machine making equal amounts of widgets. the company runs six days a week. how many widgets does each machine make.

37. Farmer Fran has 35 hens. Each hen lays a dozen eggs a day. Fran packs the eggs into packs of ten. How many packs of eggs does she pack per day?

38. ReadOn Publishers gives free books to schools every year on the last day of the year. They have 900 books for this year’s giveaway. 18 schools have applied for the free books. How many should each school get if they are evenly distributed?

39. Coach Cindy is meeting with each player for practice individually. Each player will get 15 minutes with the coach. Coach Cindy has 2 hours for this on Saturday. How many players can she meet with?

40. Dr. Bea Well has 120 patients. ¼ of them wear glasses. How many of her patients don’t wear glasses?

41. Lucy has 24 stuffed animals. She loves elephants, and one-third of her stuffed animals are elephants. Half of the elephants are gray. How many elephants does she have?

42. Annie collects seashells. She has 120 shells in her collection. They are from both the Atlantic Ocean and the Pacific Ocean. ¾ of the shells are from the Atlantic Ocean. How many shells are from the Pacific Ocean?

43. Bill has 7/8 of his homework done. Andy has 9/10 of his homework done. They have the same amount of homework. Who has more homework done?

44. Jose was offered 2/5 of a jumbo chocolate bar or 3/6 of the same bar. He loves chocolate. Which should he choose if he wants the most chocolate?

45. Janelle has 6 notebooks for school. Donnie has 1/3 more than Janelle. How many notebooks do Janelle and Donnie have all together?

46. Tonya found two small interesting stones. The black one weighs 0.3 of an ounce. The red one weighs 0.09 of an ounce. Which stone weighs more?

47. Leah has a baseball bat that is 2 and a half feet long. Bryson has a bat that is 28 inches long and another one that is 2 feet and 5 inches long. Who has the longest bat?

48. Mr. Smith’s class collected coins in a big jar for 6 months. Their coins weighed 2 pounds and 8 ounces. Ms. Smith’s class did the same thing. Their coins weighed 2 ½ pounds. Whose coins weighed more?

49. The track team was practicing for the big meet. Tim ran for 25 minutes every day for 5 days. Tom ran an hour every day for 3 days. Who spent the most time running?

50. The Jones family left for the airport at 10:00 a.m. for vacation. Their flight leaves at 12:30 p.m. They stopped twice for 10 minutes each time. They got to the airport at 11:30 p.m. How much time did they spend driving?

Enjoying these fourth grade math word problems? Check out our fourth grade hub for even more resources.

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50 Third Grade Math Word Problems of the Day

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• G4 Worksheets

" class="arrow-title-img"> Math word problems for grade 4 worksheets - Grade 4 Math problem solving strategies worksheets

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Which math skills will 4 th graders benefit from as they engage in solving math word problems for grade 4 worksheets?

Get more contents on fourth grade..., multi-step word problems worksheets grade 4 pdf.

Available here are special math word problems for grade 4 worksheets designed to give your kids an opportunity to practice grade 4 math in an easy, fun and engaging way. In line with this, we have created simple grade 4 math problem solving strategies that will enhance fluency when solving grade 4 math concepts in the classroom and in our daily lives. 

Also, our multi-step word problems worksheets grade 4 pdf is here to guide kids on an orderly and correct way of solving problems that require the use of more than one math operation. This idea of designing multi-step problems worksheets will enhance kid’s attention during the solving process.

By so doing, they will be encouraged to understand that there are simple steps and an orderly way of solving some seemingly lengthy and difficult problems.

Adding two numbers up to five digits

Adding two numbers up to seven digits

Estimating sums

Subtracting two numbers up to five digits

Subtracting numbers up to seven digits

Estimating differences

Multiplying two digits number by one digit number

3-digits-or-4-digits-number-by-1-digit-numbers-multiplication-word-problems

Estimating products

Multiplying two digits number by two digits number

Multiplying a lager number by two digits number

Multiplying three or more numbers

Comparing numbers using multiplication

Division facts up to ten

Fraction of whole numbers

Adding three or more decimals

Adding an subtracting decimals

Multiply 3 digits or 4 digits number by 1 digit number

• 3 digits or 4 digits number by 1 digit numbers multiplication word problems
• Adding 3 or more decimals word problems grade 4
• Adding and subtracting decimals word problems
• Adding two numbers up to five digits word problems grade 4
• Adding two numbers up to seven digits word problems grade 4

Download 4th-grade worksheets by topic

Engage your kids in this resource and discover for yourselves, which math skills will 4 th graders benefit from as they engage in solving math word problems for grade 4 worksheets?

In the first place, as your 4 th graders strive to practice how to apply grade 4 math concepts in real life, they will equally gain genuine math skills that will benefit them throughout their academic careers. Some of these skills include: logical reasoning skills, estimation, comparison, place value and number sense skills.

Secondly, given that these worksheets have been designed purposely for 4 th graders, our word problems have been focused on addition, subtraction, multiplication and division, fraction, decimals and multi-step word problems.

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Maths Problems With Answers - Grade 4

A set of Maths problems with answers for grade 4 are presented. Also Solutions and explanations are included.

• Jim drove 768 miles of a 1200 miles journey. How many more miles does he need to drive to finish his journey?
• There are 123 boxes of sweets in a store. There are 25 sweets in each box. How many sweets are in the store?
• There are 365 days in one year, and 100 years in one century. How many days are in one century?
• Billy read 2 books. He read the first one in one week with 25 pages everyday. He read the second book in 12 days with 23 pages everyday. What is the total number of pages that Billy read?
• 123 school girls are to be transported in small vans. Each van can carry 8 girls only. What is the smallest possible number of vans that are needed to transport all 123 school girls?
• John had $100 to buy drinks and sandwiches for his birhtday party. He bought 5 small boxes of drinks at $4 each box and 8 boxes of sandwiches at $6 each box. How much money was left after the shopping?
• A factory produces 5500 toys per week. If the workers at this factory work 4 days a week and if these workers make the same number of toys everyday, how many toys are produced each day?
• Tom, Julia, Mike and Fran have 175 cards to use in a certain game. They decided to share them equally. How many cards should each one take and how many cards are left?
• Sam, Carla and Sarah spent on afternoon collecting sea shells. Sam collected 11. If we add the number of sea shells collected by Sam and Carla, the total would be 24. If we add the number of sea shells collected by Carla and Sarah, the total would be 25 shells. How many shells did each one collect?
• Mr Joshua runs 6 kilometers everyday from Monday to Friday. He also runs 12 kilometers a day on Saturday and Sunday. How many kilometers does Joshua run in a week?
• Tom and Bob are brothers and they each had the same amount of money which they put together to buy a toy. The cost of the toy was $22. If the cashier gave them a change of 6$, how much money did each have?
• John has 5 boxes of sweets. One group of boxes has 5 sweets in each box. The second group of boxes has 4 sweets in each box. John has a total of 22 sweets. How many boxes of each type John has?(Hint: use table)
• There is a total of 16 chickens and rabbits in a farm. The total number of legs (chickens and rabbits) is equal to 50. How many chickens and how many rabbits are there?(Hint:use a table)
• There are 4 more chickens than rabbits in a farm. The total number of legs (chickens and rabbits) is equal to 44. How many chickens and how many rabbits are there?(Hint:use a table)

Answers to the Above Questions

• a) UK b) Russia c) 7,500,148 d) 49,839,760 e) Russia, Canada, USA, China, India, Uk.
• 3075 sweets
• 36,500 days in one century
• 16 vans (no decimal values)
• 1375 toys per day
• 43 each and 3 left
• 80 cm squared
• Sam: 11, Carla: 13 and Sarah: 12
• 54 kilometers
• 2 boxes with 5 sweets each and 3 boxes with 4 sweets each
• 7 chickens and 9 rabbits
• 10 chickens and 6 rabbits

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Division Worksheets Grade 4 Solving Division Problems

Welcome to our Division Worksheets Grade 4 page. Here you will find a wide range of free 4th Grade Division Worksheets, which will help your child learn to solve division problems across a range of different contexts.

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Division Worksheets Grade 4

Solving division problems.

The worksheets on this page have been designed to support your child on their division journey from the start of 4th grade to the end.

The first two sets of sheets involve working out division problems where there is no remainder.

The second two sets involve working out harder division problems with remainders.

In order to solve the second sets of word problems, the remainder needs to be rounded up or down, depending on the context.

Each set of division word problems has been subdivided into 3 worksheets:

• Sheet A - an easier worksheet;
• Sheet B - a medium worksheet;
• Sheet C - a harder worksheet.

Division Worksheets Grade 4 - Worksheets

Set 1 - solving division problems with no remainder..

• Division Problems 4.1 Sheet A
• PDF version
• Division Problems 4.1 Sheet B
• Division Problems 4.1 Sheet C

Set 2 - solving division problems with no remainder.

• Division Problems 4.2 Sheet A
• Division Problems 4.2 Sheet B
• Division Problems 4.2 Sheet C

Set 3 with remainders

This set involves solving division problems with a remainder. The answer needs to be rounded up or down, depending on the context.

• Division Problems 4.3 Sheet A
• Division Problems 4.3 Sheet B
• Division Problems 4.3 Sheet C

Set 4 with remainders

• Division Problems 4.4 Sheet A
• Division Problems 4.4 Sheet B
• Division Problems 4.4 Sheet C

Looking for some easier Division worksheets

Our 3rd grade division worksheets are similar to those on this page but at an easier level.

The link below will take you to our division worksheets for 3rd grade.

• Division Worksheets Grade 3 Word Problems
• Division Facts to 10x10 Worksheets
• Long Division Worksheets 3rd Grade

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

More Division Worksheets

• Divide a multi-digit number by a single digit;
• Use remainders when dividing;
• Calculate division facts related to multiplication facts.
• Divding by Multiples of 10 and 100 Worksheets
• 4th Grade Long Division Worksheets
• Division Facts Worksheets (randomly generated)

More Fourth Grade Math Problems

Here is our set of 4th grade math problems to help your child with their problem solving skills.

Each problem sheet comes complete with answers, and is available in both standard and metric units where applicable.

Many of the problems are based around 'real-life' problems and data such as the world's heaviest animals.

Using these sheets will help your child to:

• apply their addition, subtraction and problem solving skills;
• apply their knowledge of rounding and place value;
• solve a range of 'real life' problems;
• attempt more challenging longer problems.

Using the problems in this section will help your child develop their problem solving and reasoning skills.

These sheets involve solving one or two more challenging longer problems.

• 4th Grade Math Problems

These sheets involve solving many 'real-life' problems involving data.

• 4th Grade Math Word Problems

These sheets involve solving a range of multiplciation problems.

• Multiplication Word Problems 4th Grade

Fourth Grade Math Games

Here you will find a range of free printable 4th Grade Math games. All children like to play Math games, and you will find a good range of Grade 4 Math Games here for your child to play and enjoy.

The following games involve different 4th Grade Math activities which you and your child can enjoy together.

All the free 4th Grade Math Worksheets in this section support the Elementary Math Benchmarks for Fourth Grade.

• Math Games 4th Grade
• 4th Grade Math Puzzles

Here you will find a range of printable 4th grade math puzzles for your child to enjoy.

The puzzles will help your child practice and apply their addition, subtraction, multiplication and division facts as well as developing their thinking and reasoning skills in a fun and engaging way.

Using these puzzles will help your child to:

• learn and practice their addition facts;
• practice adding both positive and negative numbers;
• practice their subtraction facts;
• practice multiplication and division facts;
• develop problem solving skills and reasoning.

All the puzzles support elementary math benchmarks for 4th grade.

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• Inspiration

5 Trigonometry Math Problems with Triangles

• Math Problems / Geometry / Trigonometry
• 4 mins read
• high school , Triangle

In this blog, we are discussing 5 trigonometry math problems with triangles and their solutions using trigonometry which include several properties of triangles like cosine rule, sine rule, projection formula, etc

Table of Contents

Problem 1: Radius of the Circumcircle of the Triangle

Trigonometry Math Problems with Triangles 1: Find the radius of the circumcircle of the triangle

Triangle ABC’s sides are AB = 9 cm, BC = 8 cm, and AC = 6 cm. Then find the radius of the circumcircle of the triangle

Solution: Radius of the circumcircle of the triangle

Let’s assume ∠BAC = x

Apply the Cosine rule in triangle ABC

BC² = AB² + AC² – 2 × AB × AC × cos ∠BAC

⇒ 8² = 9² + 6² – 2 × 9 × 6 × cos x

⇒ 64 = 81 + 36 – 108cos x

⇒ 53 = 108cos x

⇒ cos x = 53/108

sin² x + cos² = 1

⇒ sin² x + 53²/108² = 1

⇒ sin² x + 53²/108²

⇒ sin² x = 1 – 2809/11664 = 8855/11664

⇒ sin x = √8855/108

Now use the Sine rule

Diameter of Circumcircle = BC/sin x

Diameter of Circumcircle = 8/(√8855/108) = 864/√8855 cm

Radius of the Circumcircle = 8/(√8855/108) = 432/√8855 cm

Problem 2: Length of the Median

Trigonometry Math Problems with Triangles 2: Find the length of the median of the triangle

Triangle ABC’s sides are AB = 12 cm, BC = 10 cm, and AC = 8 cm. Then find the length of the median of the triangle ABC from A to side BC.

Solution: Length of the median.

Let’s assume AP = y and ∠ACB = x

AB² = AC² + BC² – 2 × AC × BC × cos ∠ACB

⇒ 12² = 8² + 10² – 2 × 8 × 10 × cos x

⇒ 144 = 64 + 100 – 160cos x

⇒ 160cos x = 20

⇒ cos x = 1/8

Apply the Cosine rule in triangle APC

AP² = AC² + PC² – 2 × AC × PC × cos ∠ACB

⇒ y² = 8² + 5² – 2 × 8 × 5 × cos x

⇒ y² = 64 + 25 – 80 × 1/8

⇒ Length of the median = AP = y = √79 cm

Problem 3: Find the Height of the Triangle

Trigonometry Math Problems with Triangles 3: Find the Height of the Triangle

From triangle ABC, AB = 12 cm, ∠BAC = 30° and ∠ABC = 45°, Then find the height of the triangle

Solution: Height of the Triangle

Let’s assume AD = a and BD = b

From figure,

tan ∠BAC = CD/AD

⇒ tan 30 = h/a

⇒ 1/√3 = h/a

tan ∠ABC = CD/BD

⇒ tan 45 = h/b

a + b = 12 = h√3 + h

⇒ h(√3 + 1) = 12

⇒ h = 12/(√3 + 1)

⇒ h = 6√3 – 6 cm

⇒ Height of the Triangle, h = 6√3 – 6 cm

Problem 4: Area of the Irregular Polygon

Trigonometry Math Problems with Triangles 4: Find the area of the Irregular Polygon formed by combining 4 equal squares.

An L-shaped Irregular polygon is inscribed inside the right-angle triangle ABC. The L-shaped Irregular polygon PQRST is formed by combining 4 equal squares. If AB = 13 cm and ∠ABC = 45°, then find the area of the L-shaped Irregular polygon.

Solution: Area of the Irregular Polygon

Let’s assume the sides of the square = a and ∠TPU = x

PQ = TU = TS = a (side of the square)

Apply Pythagoras theorem in triangle PTU

PT² = PU² + TU²

⇒ PT² = (2a)² + a²

⇒ PT² = 4a² + a² = 5a²

sin ∠TPU = TU/PT

⇒ sin x = a/a√5

⇒ sin x = 1/√5

cos ∠TPU = PU/PT

⇒ cos x = 2a/a√5

⇒ cos x = 2/√5

From triangle PQV

sin ∠PQV = PV/PQ

⇒ sin x = PV/a

⇒ 1/√5 = PV/a

⇒ PV = a/√5

cos ∠PQV = QV/PQ

⇒ cos x = QV/a

⇒ 2/√5 = QV/a

⇒ QV = 2a/√5

From triangle AVQ

tan ∠VAQ = VQ/AV

⇒ tan 45 = 2a/√5/AV

⇒ 1 = 2a/√5/AV

⇒ AV = 2a/√5

Apply Pythagoras theorem in triangle TSR

TR² = ST² + SR²

⇒ TR² = a² + (2a)² = a² + 4a² = 5a²

From triangle TBR

tan ∠VAQ = TR/TB

⇒ tan 45 = a√5/TB

⇒ 1 = a√5/TB

AB = AV + VP + PT + TB

⇒ AB = 2a/√5 + a/√5 + a√5 + a√5

⇒ 13 = 3a/√5 + 2a√5

⇒ 13√5 = 3a + 10a

⇒ 13√5 = 13a

Area of L-shaped Irregular polygon PQRST = 4 × Area of the Square

⇒ Area of L-shaped Irregular polygon PQRST = 4 × a² = 4 × 5

⇒ Area of L-shaped Irregular polygon PQRST = 20 cm²

Problem 5: Area of the Triangle

Trigonometry Math Problems with Triangles 5: Find the area of the triangle

From the figure, triangle ABC is a right-angled triangle, ∠BAC = 30°, ∠BPC = 60° and AP = 5 cm then find the area of the triangle ABC.

Solution: Area of the triangle

tan ∠BAC = BC/AB

⇒ tan 30° = h/(5 + x)

⇒ 1/√3 = h/(5 + x)

⇒ 5 + x = h√3

⇒ x = h√3 – 5

tan ∠BPC = BC/PB

⇒ tan 60° = h/x

⇒ (h√3 – 5)√3 = h

⇒ 3h – 5√3 = h

⇒ Height of the triangle ABC, h = (5√3)/2 cm

x = h√3 – 5 = ((5√3)/2)√3 – 5

x = 15/2 – 5

area of the triangle = (AB × BC)/2

area of the triangle = ((5 + 5/2) × (5√3)/2)/2

area of the triangle = ((15/2) × (5√3)/2)/2

area of the triangle = (75√3)/8 cm²

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Past Contests, Solutions and Results

Problems, Solutions and Results from previous years can be found in the table below. These resources can be used by students to review and attempt past contests to gain a better understanding of the contest format and level of difficulty. Educators can use these resources to help their students prepare for contests or draw inspiration from some of these questions to create teaching materials, lesson plans or quizzes.

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For the Gauss , Pascal, Cayley, and Fermat Contests, the CEMC Problem Set Generator can be used to create sets of past problems with customized topics. 

• CBSE Class 10

CBSE Class 10 Maths Competency-Based Questions With Answers 2024-25: Chapter 1 Real Numbers Download Free PDF

Cbse class 10 maths chapter 1 practice questions 2025: cbse has made available the competency-based practice questions for students of class 10. check and download the questions for cbse class 10 maths chapter 1 real numbers. .

CBSE 2024-25 Competency Based Questions With Answers: To ensure that students are learning with understanding, the Central Board of Secondary Education (CBSE) has created and released the competency-based practice questions for various subjects covered in class 10. These have been released for the academic session 2024-25. These assessment questions are critical to the learning of students. In this article we have covered the CBSE Class 10 Maths Chapter 1 Real Numbers competency-based questions. 

Assessments prove to be of great help in providing feedback about what students have actually understood. The competency-based assessments were introduced as a means to reform curriculum and pedagogical methodologies. They emphasize on the development of higher order skills such as analysis, critical thinking and problem solving. 

CBSE Class 10 Maths Chapter 1 Competency Based-Questions 

Tips to Prepare for CBSE Class 10 Mathematics Examination

1. Students must first familiarize themselves with the syllabus so as to understand which topics carry more weightage. 

2.Mathematics is a subject that demands regular practice. It is important that students practice as much as they can. 

3.Students should prepare an effective study plan and give time to all topics on the basis of their strengths and weaknesses. The schedule should also have time for revision. 

4.Students should solve the problems from CBSE Class 10 subject textbook to clear the concepts and strengthen understanding. While solving problems, students should make it a habit to show rough work clearly which will help them in the examination as well. 

CBSE Video Courses for Class 10 Students 

Class 10 students can study effectively for the exams with the help of video courses prepared by the subject matter experts. These video courses will explain the concepts in a simple and interactive manner which will help learners to understand clearly. Refer to the link below:

CBSE Class 10 Video Courses 

Also, check

CBSE Class 10 Syllabus 2024-25: Download Latest and Revised FREE PDFs

NCERT Books for Class 10 All Subjects PDF (2024-25)

NCERT Solutions for Class 10 (2024-2025) All Subjects & Chapters: Download in PDF

NCERT Rationalised Syllabus Class 10: List of Chapters & Topics Deleted from Books

CBSE Class 10 Maths MCQs: Important for 2024-2025 Exams, Download Chapter-Wise PDF

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4th Grade Math Worksheets: Addition

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Our grade 4 addition worksheets range from simple two digit addition with no regrouping through addition of multiple 6 digit addends in columns .

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