Question

The surface area of a square pyramid is found using the formula 2003-05-05-00-00_files/i0080000.jpg, where b is the length of the base and h is the height. The surface area of a square pyramid whose base is 3 feet long is 51 2003-05-05-00-00_files/i0080001.jpg. What is the height of the pyramid, in feet?

Answer 1

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 + (4*3ft / 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.