Given:
base = 3 ft
surface area = 51 ft²
height = ?
surface area of a square pyramid = B + 1/2 nbl
n = number of triangle
b = base measure
l = slant height
51 ft² = (3ft)² + 1/2 4 3ft l
51 ft² = 9ft² + (43ft / 2) l
51 ft² - 9 ft² = 12ft/2 l
42 ft² = 6 ft l
42 ft² / 6 ft = l
7 ft = l
height of the pyramid is 7 feet.
