Surface Area of Rectangular Pyramids Quick Check
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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
819 ft.2
819 ft. squared
522 ft.2
522 ft. squared
148.5 ft.2
148.5 ft. squared
299.25 ft.2
To find the surface area of a rectangular pyramid, we calculate the sum of the area of the base plus the area of the four triangular faces.
First, calculate the area of the base:
Area of a square = side^2
Area of the base = 15^2 = 225 ft^2
Next, calculate the area of each triangular face:
Area of a triangle = (1/2) * base * height
For each triangular face, the base is 15 ft and the height is 9.9 ft.
Area of each triangular face = (1/2) * 15 * 9.9 = 74.25 ft^2
There are four triangular faces, so the total area of the four faces = 4 * 74.25 = 297 ft^2
Finally, add the base area and the four triangular faces' areas:
Total surface area = 225 + 297 = 522 ft^2
Therefore, the correct response is:
522 ft.2
522 ft. squared