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Year 10
Higher

Applying Pythagoras' theorem in 3D

I can apply knowledge of Pythagoras' theorem to 3D problems.

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Share activities with pupils
New
New
Year 10
Higher

Applying Pythagoras' theorem in 3D

I can apply knowledge of Pythagoras' theorem to 3D problems.

Download all resources
Share activities with pupils

Lesson details

Key learning points

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

Common misconception

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.

Keywords

  • 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.

Pupils may benefit from using the frame of a cuboid and some string so they can physically construct the right-angled triangles within it.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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Starter quiz

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6 Questions

Q1.
The relationship between the hypotenuse and the two short sides on a right-angled triangle is known as ' theorem.
Correct Answer: Pythagoras
Q2.
Work out the the length of the hypotenuse, to 1 decimal place.
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Correct Answer: 8.1 cm, 8.1
Q3.
Work out the the length of the hypotenuse, to 1 decimal place.
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Correct Answer: 43.1 cm, 43.1
Q4.
Work out the length of the third side of the triangle, to 3 significant figures.
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Correct Answer: 25.3 cm, 25.3
Q5.
Work out the length of the third side of the triangle, to 3 significant figures.
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Correct Answer: 5.99 cm, 5.99
Q6.
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.
Correct Answer: 137, 137 yards, 137 yd

Exit quiz

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6 Questions

Q1.
Which of these are right-angled triangles?
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Correct Answer: An image in a quiz
An image in a quiz
Correct Answer: An image in a quiz
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Q2.
Given that DE = 6 cm and EH = 15 cm, what is the length of DH, to 1 decimal place?
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Correct Answer: 16.2 cm, 16.2
Q3.
Given that BG = 9 cm and GE = $$7\sqrt{2}$$ cm, what is the length of BE, to 1 decimal place?
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Correct Answer: 13.4 cm, 13.4
Q4.
If AF, FE and FH are known, which other length do we need, in order to calculate the volume of this cuboid?
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BG
BC
BE
Correct answer: EH
AG
Q5.
Given that AF = 5 cm, FE = 12 cm and FH = 15 cm, work out the length of EH.
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Correct Answer: 9 cm, 9, nine
Q6.
Given that AF = 5 cm, FE = 12 cm and FH = 15 cm, the volume of the cuboid ABCDEFGH is $$\text{ cm}^3$$
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Correct Answer: 540