Edexcel IGCSE Math A 4.8.HD Pythagoras in three dimensions

Practise 3D Pythagoras questions by finding a right triangle inside the solid, then using one or two squared-length calculations.

Exam points

Find a missing length in a cuboid or solid by identifying the relevant right triangle.
Use Pythagoras in stages when a space diagonal or hidden length is required.

[Maximum number: 3]

The diagram shows a prism ABCDEFGH with a horizontal base.

Figure for Question 4.8.HD Pythagoras’ theorem in three dimensions question 1 — Edexcel IGCSE Math A Higher

Diagram NOT accurately drawn

The base of the prism, EFGH, is a square of side 12 cm.
Trapezium ADEF is a cross section of the prism where AF and DE are vertical edges.
$D E=C H=10 \mathrm{~cm}$ $A D=B C=15 \mathrm{~cm}$

Work out the length of BE.

Give your answer correct to one decimal place.

$BG=10+\sqrt{15^2-12^2}=10+9=19$

Using $FH=\sqrt{288}=16.97\ldots$ :
$BE=\sqrt{19^2+(16.97\ldots)^2}=25.47\ldots$

Final answer:
BE=25.5

Accept 25.4 to 25.6.

Marking guidance:
- M1 for finding BG=19.
- M1 ft for using their FH to find BE.
- A1 for 25.5 within the accepted range.

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4.8.HD Pythagoras’ theorem in three dimensions question 1