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

299.25 ft.2
299.25 ft. squared

819 ft.2
819 ft. squared

148.5 ft.2
148.5 ft. squared

522 ft.2
522 ft. squared
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Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the surface area of the square pyramid, we first need to find the area of the base and the area of the four triangular faces.

1. Area of the base:
Area = side * side
Area = 15 ft * 15 ft
Area = 225 ft²

2. Area of each triangular face:
The base of each triangle is 15 ft (one side of the square base) and the height of each triangle is 9.9 ft.
Area of each triangle = (1/2) * base * height
Area of each triangle = (1/2) * 15 ft * 9.9 ft
Area of each triangle = 74.25 ft²

Since there are four triangular faces, total area of the four triangular faces = 4 * 74.25 ft² = 297 ft²

3. Total surface area of the square pyramid:
Surface area = Area of base + Total area of four triangular faces
Surface area = 225 ft² + 297 ft²
Surface area = 522 ft²

Therefore, the surface area of the square pyramid is 522 ft².

The correct answer is:
522 ft.²