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.
299.25 ft.2
148.5 ft.2
819 ft. squared.
522 ft. squared.
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To find the surface area of a square pyramid, we can use the formula:
Surface Area = base area + (1/2 * perimeter of base * slant height)
First, let's find the base area of the square pyramid:
Base area = side length * side length = 15 ft * 15 ft = 225 ft^2
Next, we need to find the slant height of the pyramid. The slant height can be calculated using the Pythagorean theorem:
Slant height = sqrt( (1/2 * side length)^2 + height^2)
Slant height = sqrt( (7.5 ft)^2 + (9.9 ft)^2)
Slant height = sqrt( 56.25 ft + 98.01 ft)
Slant height = sqrt(154.26 ft)
Slant height ≈ 12.43 ft
Now, we can calculate the surface area:
Surface Area = 225 ft^2 + (1/2 * 15 ft * 12.43 ft)
Surface Area = 225 ft^2 + (1/2 * 186.45 ft^2)
Surface Area = 225 ft^2 + 93.225 ft^2
Surface Area = 318.225 ft^2
Therefore, the surface area of the square pyramid is approximately 318.225 ft^2.
None of the given answer choices are exactly correct, but the closest one is 299.25 ft^2.