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

The area of square base = 324 m²

The length of the square side = √324 = 18

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

The formula of area of triangle = (1/2)*base* height

Calculations 

⇒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

To solve this problem we have to use the Pythagorean theorem. The longest side of the triangle is called the "hypotenuse". C² is the longest side so it is the hypotenuse . To calculate h² we have to do c² - β² = h². 
 
15² = H² + 9²

225 =H² + 81

 H² + 81 = 225

H²  = 225 - 81

H²  = 144          Take the square root of both sides

H  = √144

H = 12

Height = 12 meters. 

Option C.

Answer 2

We have to keep in mind that :- 

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

15² = H² + 9²

225 =H² + 81

 H² + 81 = 225

H²  = 225 - 81

H²  = 144          Take the square root of both sides

H  = √144

H = 12

Height = 12 meters.