Question

The base of the pyramid is a square what is the surface area if the pyramids height is 4 feet in the area of the base is 36 ft.?

Answer 1

96 ft²

Explanation:

The general formula for the surface area of a pyramid is:

SA =
`(1)/(2)`pl + B, were p = the perimeter of the base, l = the slant height and B = the area of the base

Since the area of the base is 36 ft², then each side is √36, or 6 ft. The perimeter is the sum of all the sides, so 6 x 4 = 24 ft.

Given the overall height of the pyramid is 4 feet, you can use the Pythagorean Theorem (a² + b² = c²) to find the slant height (hypotenuse) of the pyramid. Using 3 feet for 'a' and 4 feet for 'b':

3² + 4² = c² or 9 + 16 = 25

25 = c² or c = 5

SA =
`(1)/(2)`(24)(5) + 36

SA = 60 + 36 = 96 ft²