To find the surface area of the square pyramid, you need to calculate the area of the base (a square) and the area of the four triangular faces.
First, calculate the area of the base:
Side of the square base = 15 ft
Area of the square base = side^2 = 15^2 = 225 ft^2
Next, calculate the area of the four triangular faces:
Using Pythagoras, the height of the pyramid is:
h = √((15/2)^2 + 12^2) = √(7.5^2 + 12^2) = √(56.25 + 144) = √200.25 = 14.14 ft
Area of each triangular face = 1/2 * base * height
Area of each triangular face = 1/2 * 15 * 14.14 = 106.05 ft^2
Total area of four triangular faces = 4 * 106.05 = 424.20 ft^2
Now, calculate the total surface area of the square pyramid:
Surface area = Area of the base + Area of four triangular faces
Surface area = 225 + 424.20 = 649.20 ft^2
Therefore, the answer is not provided in the response options given. The closest would be 522 ft^2, but the actual surface area calculated is 649.20 ft^2.
Use the image to answer the question.
Solve for the surface area of the square pyramid.
(1 point)
Responses
299.25 ft.2
299.25 ft. squared
522 ft.2
522 ft. squared
148.5 ft.2
148.5 ft. squared
819 ft.2
819 ft. squared
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1 answer