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7.09 Pythagoras in 3D

Interactive practice questions

All edges of the following cube are $7$7 cm long.

a

Find the exact length of $EG$EG as a surd.

b

Use your answer from part (a) to find the exact length of $AG$AG in simplest surd form.

Easy
3min

A square prism has sides of length $5$5cm, $5$5cm and $9$9cm as shown.

Easy
3min

A rectangular prism has dimensions as labelled on the diagram.

Easy
7min

Sophia has a pencil box with the dimensions $12$12 cm by $8$8 cm by $6$6 cm, as shown in the figure.

Easy
3min
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Outcomes

VCMMG370 (10a)

Apply Pythagoras’ theorem and trigonometry to solving three-dimensional problems in right-angled triangles.

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