Shape and Space 9

3 marks · Normal

A pyramid has a square base PQRS, with PQ = QR = 6 cm. The vertex T is vertically above the centre of the base TSQ. The height VT = 9 cm.

Calculate the length of the edge VP from the vertex to a base corner.

Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.

Show answer

10.2 cm (±0.05)

Also accept: 10.20 cm; 10.20

Common mistakes: Forgetting the midpoint to corner distance.; Using base edge instead of half.

Show mark scheme and worked solution

Marking points

M1 · 1 mark · Finds the distance from centre to vertex P on base:

M2 · 1 mark · Applies Pythagoras’ theorem in 3D: (follow-through)

A1 · 1 mark · Correct value for VP: 10.2 cm (3 sf) (follow-through)

Worked solution

Let O be the centre of base PQRS. Each base side is 6 cm, so the distance from O to P is half of the diagonal:

Now, use Pythagoras’ theorem in 3D (vertical height 9 cm):

Give answer to 3 significant figures: