Surface Area of Rectangular Pyramids Quick Check

Question

3 of 53 of 5 Items

Question
Use the image to answer the question.

An illustration shows a pyramid with a square base. The side of the base is labeled 15 feet. The perpendicular height denoted by a right angle symbol on the lateral face from the apex to the base is labeled 9.9 feet.

Solve for the surface area of the square pyramid.

(1 point)
Responses

148.5 ft.2
148.5 ft. squared

522 ft.2
522 ft. squared

819 ft.2
819 ft. squared

299.25 ft.2

Answer 1

The surface area of a rectangular pyramid can be calculated using the formula:

Surface Area = Base Area + (1/2)Perimeter of Base * Slant Height

First, calculate the Base Area of the square base:
Base Area = s^2, where s is the side of the base
Base Area = 15^2 = 225 square feet

Next, calculate the Perimeter of the base:
Perimeter of Base = 4s, since it is a square
Perimeter of Base = 4(15) = 60 feet

Now, calculate the Slant Height using the Pythagorean Theorem with the base side and the height of the pyramid:
Slant Height = √(s^2 + h^2), where h is the height
Slant Height = √(15^2 + 9.9^2) = √(225 + 98.01) = √323.01 = 17.96 feet

Now plug the values into the formula:
Surface Area = 225 + (1/2)(60)(17.96) = 225 + 538.8 = 763.8 square feet

Therefore, the correct answer is not listed in the options provided. The correct surface area of the square pyramid is 763.8 ft^2.