Transum Software

Pythagoras' Theorem Quiz

A self marking exercise on the application of Pythagoras' Theorem.

Level 1 Level 2 Level 3 Level 4 Level 5 Exam-Style Description Help More on Pythagoras

Here are some questions which can be answered using Pythagoras' Theorem. You can earn a trophy if you get at least 14 questions correct. Each time you finish a question click the 'Check' button lower down the page to see if you got it right!
[Don't forget to include the units in your answers after question one]

1. What is the name for the longest side of a right angled triangle?

Correct Wrong

2. What is the length of the longest side of a right angled triangle if the two shorter sides are 5cm and 12cm?

Correct Wrong

3. Find the length of AB to 1 decimal place.

Correct Wrong

4. Find the length of EG to 1 decimal place.

Correct Wrong

5. Find the length of JK to 1 decimal place.

Correct Wrong

6. A rectangular swimming pool is 23m wide and 44m long. Calculate the length of a diagonal in metres to 1 decimal place.

Correct Wrong

7. A ladder is 6m long. How far from the base of a wall should it be placed if it is to reach 5m up the wall? Give your answer in metres correct to 1 decimal place

Correct Wrong

8. A tent guy line supports one of the upright tent poles. It runs from the top of the pole to a peg in the ground two and a half metres away from the base of the pole. If the guy line is 353cm long, how tall is the upright tent pole? Give your answer in centimetres correct to the nearest centimetre.

Correct Wrong

9. How long is the diagonal of an A4 size sheet of paper? The dimensions of A4 paper are 210 by 297 millimetres (8.3 inches × 11.7 inches). Give your answer in cm to one decimal place.

Correct Wrong

10. For international matches football pitches must be of regulation size. The goal lines must be between 64 and 75 metres (70 and 80 yards) long and the touchlines must be between 100 and 110 metres (110 and 120 yards).

What is the difference between the length of the diagonal of the largest acceptable pitch and the length of the diagonal of the smallest acceptable pitch? Give your answer in metres to the nearest metre.

Correct Wrong

11. Find the length of a side of a rhombus whose diagonals are of length 15km and 18km. Give your answer in kilometers correct to one decimal place.

Correct Wrong


12. Find the perimeter of this parallelogram to one decimal place.

Correct Wrong

13. The length of the diagonal of a square is 88m. How long are the sides of the square? Give your answer correct to one decimal place.

Correct Wrong


14. Find the height (h) of this isosceles triangle to one decimal place.

Correct Wrong

15. The sign says 'Keep off the grass'. Each day Michael has to get from one corner of the rectangular area of grass to the opposite corner. If the park keeper is looking he will walk along the edges but if the park keeper is not looking he will take the direct route, diagonally across the rectangle.

How much further does Michael walk on the days when the park keeper is looking? The length of the rectangular area of grass is 155m and the width is 98m. Give your answer to the nearest metre.

Correct Wrong

16. The blue squares have sides of length 31mm and the red square has sides of length 43mm. Find the distance from A to B in centimetres correct to one decimal place.

Correct Wrong

17. An irregular quadrilateral ABCD has right angles at the opposite vertices A and C. Calculate the length of the side DA if AB=35.2cm, BC=37.1cm and CD=37.2cm. Give your answers in cm to one decimal place.

Correct Wrong

18. An aeroplane flies due north for 346km then changes direction and flies east for 359km. How far is it now in a straight line from its starting position. Give your answer to the nearest kilometre.

Correct Wrong

19. A ship sails on a bearing of 045o for 260km then changes direction and sails on a bearing of 135o for 449km. Finally it then turns and sails for 191km on a bearing of 225o. How far is it now in a straight line from its starting position. Give your answer to the nearest kilometre.

Correct Wrong

20. One side of a right angled triangle is 10cm. The other two sides are both of length x. Calculate x to 3 significant figures.

Correct Wrong


This is Pythagoras' Theorem Quiz level 4. You can also try:
Level 1 Level 2 Level 3 Level 5


Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

This web site contains over a thousand free mathematical activities for teachers and pupils. Click here to go to the main page which links to all of the resources available.

Please contact me if you have any suggestions or questions.

Email address

Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician?

Comment recorded on the 11 January 'Starter of the Day' page by S Johnson, The King John School:

"We recently had an afternoon on accelerated learning.This linked really well and prompted a discussion about learning styles and short term memory."

Comment recorded on the 19 October 'Starter of the Day' page by E Pollard, Huddersfield:

"I used this with my bottom set in year 9. To engage them I used their name and favorite football team (or pop group) instead of the school name. For homework, I asked each student to find a definition for the key words they had been given (once they had fun trying to guess the answer) and they presented their findings to the rest of the class the following day. They felt really special because the key words came from their own personal information."

Featured Activity

Maths Mind Reader

Maths Mind Reader

This spectacular magic trick never fails to amaze people of all ages assuming they can add and subtract very simple numbers. The mathematics comes in finding out how the trick works.


There are answers to this exercise but they are available in this space to teachers, tutors and parents who have logged in to their Transum subscription on this computer.

A Transum subscription unlocks the answers to the online exercises, quizzes and puzzles. It also provides the teacher with access to quality external links on each of the Transum Topic pages and the facility to add to the collection themselves.

Subscribers can manage class lists, lesson plans and assessment data in the Class Admin application and have access to reports of the Transum Trophies earned by class members.

If you would like to enjoy ad-free access to the thousands of Transum resources, receive our monthly newsletter, unlock the printable worksheets and see our Maths Lesson Finishers then sign up for a subscription now:


Go Maths

Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school.

Maths Map

Are you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic.


If you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows:

Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.


©1997-2018 WWW.TRANSUM.ORG

Description of Levels



Level 1 - Finding the hypotenuse

Level 2 - Finding a shorter side

Level 3 - Mixed questions

Level 4 - Pythagoras Theorem quiz

Level 5 - Three dimensional Pythagoras and Trigonometry

Exam Style questions requiring an application of Pythagoras' Theorem and trigonometric ratios to find angles and lengths in right-angled triangles.

Pythagoras' Theorem

To find the longest side (hypotenuse) of a right-angled triangle you square the two shorter sides, add together the results and then find the square root of this total.

To find a shorter side of a right-angled triangle you subtract the square of the other shorter side from the square of the hypotenuse and then find the square root of the answer.


Pythagoras Example

AB2 = AC2 - BC2
AB2 = 4.72 - 4.12
AB2 = 22.09 - 16.81
AB2 = 5.28
AB = √5.28
AB = 2.3m (to one decimal place)

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly.