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.
522 ft.2
522 ft. squared
819 ft.2
819 ft. squared
148.5 ft.2
148.5 ft. squared
299.25 ft.2
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To find the surface area of a square pyramid, we need to calculate the area of the base and the area of each of the four triangular faces.
1. Area of the base:
Since the base is a square, we can find the area by squaring the side length. In this case, the side is 15 feet, so the area of the base is 15^2 = 225 square feet.
2. Area of each triangular face:
The area of a triangle can be calculated using the formula: Area = 0.5 * base * height.
First, we need to find the slant height of the pyramid by using the Pythagorean theorem:
slant height = sqrt((1/2 * base)^2 + height^2)
slant height = sqrt((1/2 * 15)^2 + 9.9^2)
slant height = sqrt(112.5 + 98.01)
slant height ≈ 14.1 feet
Now, we can calculate the area of each triangular face:
Area = 0.5 * base * slant height
Area = 0.5 * 15 * 14.1
Area ≈ 105.75 square feet
Since there are four triangular faces on a square pyramid, the total surface area is:
Total surface area = base area + 4 * triangle area
Total surface area = 225 + 4 * 105.75
Total surface area = 225 + 423
Total surface area = 648 square feet
Therefore, the surface area of the square pyramid is 648 square feet.
I apologize for the mistake in my previous calculation. Let's correct that and find the surface area of the square pyramid.
1. Area of the base:
The area of the square base is 15 feet x 15 feet = 225 square feet.
2. Area of each triangular face:
The slant height of the pyramid is approximately 14.1 feet.
The area of each triangular face is 0.5 x base x height.
The base of each triangle is 15 feet and the height is 9.9 feet.
Area of each triangular face = 0.5 x 15 x 9.9 = 74.25 square feet.
Since there are four triangular faces on a square pyramid, the total surface area is:
Total surface area = base area + 4 * triangle area
Total surface area = 225 + 4 x 74.25
Total surface area = 225 + 297
Total surface area = 522 square feet
Therefore, the correct surface area of the square pyramid is 522 square feet.