Question

In the square pyramid shown below, the area of each triangle is 135 square meters and the area of the base is 324 square meters. What is the height of the pyramid?
A.)18 meters
B.)15 meters
C.)12 meters
D.)9 meters

Answer 1

Area of square base = 324 m²

Length of the square side = √324 = 18

The side of the square is the base of the triangle.

Area of triangle = (1/2)*base* height

135 = (1/2)*18* h

135 = 9h

135/9 = h

15 = h

height = 15 m


To get the height of the Pyramid, the height of the Triangle and half the length of the side of the square form a right angled triangle.

Hypotenus = 15
Half length of square = 18/2 = 9
Height of Pyramid = H

By Pythagoras' Theorem:

15² = H² + 9²

225 =H² + 81

 H² + 81 = 225

H²  = 225 - 81

H²  = 144          Take square root of both sides

H  = √144

H = 12

Height = 12 meters.

Option C.