Worksheets: pythagorean theoremPolygons · grades 7-8

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Answer key · group A · for the teacher · sheet no. 204 517

Pythagorean theorem

1.D. 10, 24, 263 · 3 + 3 · 3 = 18 ≠ 16 = 4 · 4 ;6 · 6 + 8 · 8 = 100 ≠ 121 = 11 · 11 ;9 · 9 + 40 · 40 = 1681 ≠ 1849 = 43 · 43 ;√(10 · 10 + 24 · 24) = √676 = 26

2.18 cm30 · 30 − 24 · 24 = 324 ;18 · 18 = 324

3.3 m3.05 · 3.05 − 0.55 · 0.55 = 9 ;3 · 3 = 9

4.√53 mm7 · 7 + 2 · 2 = 53 ;√53

5.34 cm16 · 16 + 30 · 30 = 1156 ;34 · 34 = 1156

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Answer key

Quiz

Pythagorean theorem

GroupAB

Name Date Score / 15

1.Which set could be the side lengths of a right triangle?Below are four sets of three lengths (in centimetres).(3 pt)

A.20, 21, 29B.18, 24, 32C.3, 4, 6D.16, 30, 36

2.A right triangle has a hypotenuse of 34 cm and one leg of 16 cm. How many centimetres is the other leg?(3 pt)

3.A 3.7 m ladder leans against a vertical wall with its foot 1.2 m from the wall. How high up the wall does it reach?(3 pt)

4.Give the exact answer.A right triangle has a hypotenuse of 9 m and one leg of 5 m. How long is the other leg?(2 pt)

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Group B

Quiz

Pythagorean theorem

GroupAB

Name Date Score / 15

1.Which set could be the side lengths of a right triangle?Below are four sets of three lengths (in centimetres).(3 pt)

A.3, 3, 4B.6, 8, 11C.9, 40, 43D.10, 24, 26

2.A right triangle has a hypotenuse of 30 cm and one leg of 24 cm. How many centimetres is the other leg?(3 pt)

3.A 3.05 m ladder leans against a vertical wall with its foot 0.55 m from the wall. How high up the wall does it reach?(3 pt)

4.Give the exact answer.A right triangle has legs of 7 mm and 2 mm. How long is the hypotenuse?(2 pt)

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Group A

Sheet settings

Quiz6 questions2 groups1 topic

Sheet no.204 517The number is only shown here and on the answer key - never on the student sheet. The same number with the same topics gives the same sheet.

answer key at the endall groups

Quiz

Pythagorean theorem

GroupAB

Name Date Score / 15

1.Which set could be the side lengths of a right triangle?Below are four sets of three lengths (in centimetres).(3 pt)

A.3, 3, 4B.6, 8, 11C.9, 40, 43D.10, 24, 26

2.A right triangle has a hypotenuse of 30 cm and one leg of 24 cm. How many centimetres is the other leg?(3 pt)

3.A 3.05 m ladder leans against a vertical wall with its foot 0.55 m from the wall. How high up the wall does it reach?(3 pt)

4.Give the exact answer.A right triangle has legs of 7 mm and 2 mm. How long is the hypotenuse?(2 pt)

5.A right triangle has legs of 16 cm and 30 cm. How many centimetres is the hypotenuse?(2 pt)

6.The diagonal of a rectangle is 30 cm long, and one of its sides is 24 cm long. What is its area?(2 pt)

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Answer key · group A · for the teacher · sheet no. 204 517

Pythagorean theorem

1.D. 10, 24, 263 · 3 + 3 · 3 = 18 ≠ 16 = 4 · 4 ;6 · 6 + 8 · 8 = 100 ≠ 121 = 11 · 11 ;9 · 9 + 40 · 40 = 1681 ≠ 1849 = 43 · 43 ;√(10 · 10 + 24 · 24) = √676 = 26

2.18 cm30 · 30 − 24 · 24 = 324 ;18 · 18 = 324

3.3 m3.05 · 3.05 − 0.55 · 0.55 = 9 ;3 · 3 = 9

4.√53 mm7 · 7 + 2 · 2 = 53 ;√53

5.34 cm16 · 16 + 30 · 30 = 1156 ;34 · 34 = 1156

6.432 cm²30 · 30 − 24 · 24 = 324 ;18 · 18 = 324 ;24 · 18 = 432

The method lists the solution steps - handy when going through the sheet with the class.

Maths worksheets · phiboard.comsheet no. 999 999 · answer key, page 10 of 10

Quiz

Pythagorean theorem

GroupAB

Name Date Score / 15

1.Which set could be the side lengths of a right triangle?Below are four sets of three lengths (in centimetres).(3 pt)

A.20, 21, 29B.18, 24, 32C.3, 4, 6D.16, 30, 36

2.A right triangle has a hypotenuse of 34 cm and one leg of 16 cm. How many centimetres is the other leg?(3 pt)

3.A 3.7 m ladder leans against a vertical wall with its foot 1.2 m from the wall. How high up the wall does it reach?(3 pt)

4.Give the exact answer.A right triangle has a hypotenuse of 9 m and one leg of 5 m. How long is the other leg?(2 pt)

5.A right triangle has legs of 12 cm and 16 cm. How many centimetres is the hypotenuse?(2 pt)

6.A rectangle has a side of 24 mm and a diagonal of 26 mm. What is its area?(2 pt)

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Answer key · group B · for the teacher · sheet no. 204 517

Pythagorean theorem

1.A. 20, 21, 29√(20 · 20 + 21 · 21) = √841 = 29 ;18 · 18 + 24 · 24 = 900 ≠ 1024 = 32 · 32 ;3 · 3 + 4 · 4 = 25 ≠ 36 = 6 · 6 ;16 · 16 + 30 · 30 = 1156 ≠ 1296 = 36 · 36

2.30 cm34 · 34 − 16 · 16 = 900 ;30 · 30 = 900

3.3.5 m3.7 · 3.7 − 1.2 · 1.2 = 12.25 ;3.5 · 3.5 = 12.25

4.2√14 m9 · 9 − 5 · 5 = 56 ;√56 ;√56 = √4 · √14 = 2√14

5.20 cm12 · 12 + 16 · 16 = 400 ;20 · 20 = 400

6.240 mm²26 · 26 − 24 · 24 = 100 ;10 · 10 = 100 ;24 · 10 = 240

The method lists the solution steps - handy when going through the sheet with the class.

Maths worksheets · phiboard.comsheet no. 999 999 · answer key, page 10 of 10

What goes on the sheet: pythagorean theorem

The generator draws questions from 6 question types in this topic. Every quiz group gets the same types in the same order, only with different numbers, and a practice sheet goes from easier to harder.

Hypotenuse from Pythagoras
A rectangle from its diagonal (Pythagorean theorem)
Pythagorean theorem - an answer with a root
A leg from Pythagoras
Side lengths of a right triangle
Word problem: a ladder against a wall

What the section covers in the curriculum: Pythagorean theorem, diagonal of a square and height of an equilateral triangle, areas of polygons, a length from the area, calculations in rhombi and trapezia, converting units of area

Students can also practise online - the same question types, with step-by-step solutions: Exercises: pythagorean theorem →

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