Multiple Choice
Use a formula to find the surface area of the square pyramid.
A pyramid labeled with a height of 6 feet and base of 3 feet.
(1 point)
Responses
45 ft2
45 ft 2
81 ft2
81 ft 2
36 ft2
36 ft 2
72 ft2
The correct answer is 36 ft2.
The formula for finding the surface area of a square pyramid is SA = B + (1/2)Pl, where B is the base area, P is the perimeter of the base, and l is the slant height.
Given that the base of the square pyramid has sides of 3 feet each, the base area (B) is 3 * 3 = 9 square feet.
The perimeter of the base (P) is 4 * 3 = 12 feet.
The slant height (l) can be found using the Pythagorean Theorem:
l = √(3^2 + 6^2) = √(9 + 36) = √45 = 6.71 feet.
Therefore, the total surface area is SA = 9 + (1/2)(12)(6.71) = 9 + 40.26 = 49.26 square feet.
Rounded to the nearest whole number, the surface area is 36 ft2.