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Pythagorean Probe

Use Pythagoras' Theorem to help find all of the measurements of these right angles triangles.

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This is level 4: given two measurements. The diagrams are not drawn to scale. Include the letters 'cm' when labelling sides but the units of perimeters and areas are already typed for you.

1

Perimeter =

cm

Area =

cm2

2

Perimeter =

cm

Area =

cm2

3

Perimeter =

cm

Area =

cm2

4

Perimeter =

cm

Area =

cm2

5

Perimeter =

cm

Area =

cm2

6

Perimeter =

cm

Area =

cm2

Check

This is Pythagorean Probe level 4. You can also try:
Level 1 Level 2 Level 3 Level 5 Level 6

Instructions

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.

Why am I learning this?

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 14 September 'Starter of the Day' page by Trish Bailey, Kingstone School:

"This is a great memory aid which could be used for formulae or key facts etc - in any subject area. The PICTURE is such an aid to remembering where each number or group of numbers is - my pupils love it!
Thanks"

Comment recorded on the 17 November 'Starter of the Day' page by Amy Thay, Coventry:

"Thank you so much for your wonderful site. I have so much material to use in class and inspire me to try something a little different more often. I am going to show my maths department your website and encourage them to use it too. How lovely that you have compiled such a great resource to help teachers and pupils.
Thanks again"

Whose Idea Was This?

Did you enjoy doing this 'Pythagorean Probe' activity? Are you curious about who originally came up with this idea in Maths? Discover more about one of the mathematicians who is associated with this concept.

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Arrange the given digits one to nine to make three numbers such that two of them add up to the third. This is a great puzzle for practicing standard pen and paper methods of three digit number addition and subtraction.

Answers

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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.

Teachers

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Description of Levels

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Pythagoras' Theorem Exercise - This would be a good place to start if you are a Pythagoras beginner.

Level 1 - Given the lengths of two sides

Suitable for
Years 8 to 10

Level 2 - Given two sides in different units

Level 3 - Given one short side and the area

Level 4 - Given two measurements

Suitable for
Years 11 to 13

Level 5 - Given algebraic expressions for sides

Level 6 - Given expressions for the perimeter and area

Exam Style Questions - A collection of problems in the style of GCSE or IB/A-level exam paper questions (worked solutions are available for Transum subscribers).

More on this topic including lesson Starters, visual aids, investigations and self-marking exercises.

This exercise was inspired by a recource shared on Twitter by Nathan Day @nathanday314

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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Curriculum Reference

See the National Curriculum page for links to related online activities and resources.

Help

Did you do the main Pythagoras' Theorem Exercise yet? This is the video that mas made to help you with that exercise.

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. You can double-click the 'Check' button to make it float at the bottom of your screen. A tick or a cross will only appear if something has been typed into all of the input boxes for that question.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

Log in Sign up

This exercise was inspired by a recource shared on Twitter by Nathan Day @nathanday314

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