Question

Point O is directly above the centre of

the base.
a) Work out the length of AC.
b) Work out the perpendicular height
of the pyramid.
Give each of your answers to 3 s.f.

Answer 1

The length of AC is 26.87 cm and the perpendicular height of the pyramid is 95.6 cm

a) Work out the length of AC.

From the question, we have the following parameters that can be used in our computation:

The pyramid

The length of the segment AC can be calculated using the following Pythagoras theorem

AC² = 19² + 19²

This gives

AC = 19√2

So, we have

AC = 26.87

b) Work out the perpendicular height of the pyramid.

Here, we have

tan(82) = height/(1/2 AC)

tan(82) = height/(1/2 * 26.87)

This gives

height = (1/2 * 26.87) * tan(82)

Evaluate

height = 95.6

Hence, the perpendicular height of the pyramid is 95.6 cm