Applying Pythagoras' theorem in 3D | Maths | Quizalize & Oak National Academy

Starter quiz

The relationship between the hypotenuse and the two short sides on a right-angled triangle is known as ______' theorem.

'Pythagoras' ✓
Work out the the length of the hypotenuse, to 1 decimal place.

'8.1 cm' ✓
Work out the the length of the hypotenuse, to 1 decimal place.

'43.1 cm' ✓
Work out the length of the third side of the triangle, to 3 significant figures.

'25.3 cm' ✓
Work out the length of the third side of the triangle, to 3 significant figures.

'5.99 cm' ✓
A football pitch is 115 yards by 74 yards. What is the distance diagonally from one corner flag to the other? Give your answer to the nearest yard.

'137' ✓

Which of these are right-angled triangles?
Given that DE = 6 cm and EH = 15 cm, what is the length of DH, to 1 decimal place?

'16.2 cm' ✓
$Given that BG = 9 cm and GE = <Math>7\sqrt{2}</Math> cm, what is the length of BE, to 1 decimal place?$

Given that BG = 9 cm and GE = $7\sqrt{2}$ cm, what is the length of BE, to 1 decimal place?

'13.4 cm' ✓
If AF, FE and FH are known, which other length do we need, in order to calculate the volume of this cuboid?

BG

BC

BE

EH ✓

AG
Given that AF = 5 cm, FE = 12 cm and FH = 15 cm, work out the length of EH.

'9 cm' ✓
$Given that AF = 5 cm, FE = 12 cm and FH = 15 cm, the volume of the cuboid ABCDEFGH is <span class="blank">______</span> <Math>\text{ cm}^3</Math>$

Given that AF = 5 cm, FE = 12 cm and FH = 15 cm, the volume of the cuboid ABCDEFGH is ______ $\text{ cm}^3$

'540 ' ✓

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For packing efficiency, it can be useful to know the length of the longest diagonal
This would be from a bottom corner of a rectangular box, to the opposite top corner
You can construct a right-angled triangle to calculate this
You will need to know the length of the diagonal of the base of the box
There is a formula you can deduce to calculate the longest diagonal

Pythagoras' theorem cannot be applied to 3D shapes.

Pupils may benefit from imaging the cuboid is 'sliced' through and a triangle drawn on the now visible face.

Hypotenuse - The hypotenuse is the side of a right-angled triangle which is opposite the right angle.
Pythagoras' theorem - Pythagoras’ theorem states that the sum of the squares of the two shorter sides of a right-angled triangle is equal to the square of the hypotenuse.
Cross-section - A cross-section is a 2D face made from cutting straight through any plane of a 3D object.