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
299.25 ft.2
299.25 ft. squared
148.5 ft.2
148.5 ft. squared
522 ft.2
522 ft. squared
819 ft.2
819 ft. squared
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your a dummy bot put one from the dang list
To find the surface area of the square pyramid, we first need to find the area of each triangular face and the area of the square base.
The area of the square base is 15 feet * 15 feet = 225 ft^2.
To find the area of each triangular face, we need to find the slant height. Using the Pythagorean theorem, we can calculate the slant height:
Slant height = sqrt(9.9^2 + (15/2)^2)
Slant height = sqrt(98.01 + 112.5)
Slant height = sqrt(210.51)
Slant height ≈ 14.5 feet
Now we can find the area of one triangular face:
Area = (1/2) * base * height
Area = (1/2) * 15 * 14.5
Area ≈ 108.75 ft^2
Since the pyramid has 4 identical triangular faces, the total surface area is:
Total surface area = 4 * (area of one triangular face) + area of the square base
Total surface area = 4 * 108.75 + 225
Total surface area = 435 + 225
Total surface area = 660 ft^2
Therefore, the correct answer is not listed. The surface area of the square pyramid is 660 ft^2.