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
⇒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.