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
148.5 ft.2
148.5 ft. squared
299.25 ft.2
299.25 ft. squared
819 ft.2
819 ft. squared
522 ft.2
522 ft. squared
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To find the surface area of the rectangular pyramid, you need to calculate the area of the base (which is a square) and the area of the four triangular faces.
1. Area of the base (square):
Area = side^2
Area = 15^2
Area = 225 square feet
2. Area of one triangular face:
Area = 0.5 * base * height
Area = 0.5 * 15 * 9.9
Area = 74.25 square feet
Since there are four triangular faces, the total area of the triangular faces is:
Total triangular faces area = 4 * 74.25
Total triangular faces area = 297 square feet
Now, to find the total surface area:
Surface area = base area + total triangular faces area
Surface area = 225 + 297
Surface area = 522 square feet
Therefore, the surface area of the rectangular pyramid is 522 ft^2.
The correct answer is:
522 ft.2
522 ft. squared