Surface Area of Pyramids Quick Check
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Question
What is the surface area of a square pyramid where the base edge is 8 ft. and the slant height is 16 ft.?(1 point)
Responses
256 ft.2256 ft. squared
320 ft.2
320 ft. squared
512 ft.2512 ft. squared
To find the surface area of a square pyramid, you need to know the length of the base edge and the slant height.
The surface area can be calculated using the formula:
Surface Area = Base Area + (1/2 × Perimeter of the base × Slant Height)
In this case, the base of the pyramid is square, so the base area is equal to the side length squared:
Base Area = (8 ft)^2 = 64 ft^2
The perimeter of the base is equal to 4 times the length of one side:
Perimeter of the base = 4 × 8 ft = 32 ft
Now, substitute the values into the formula:
Surface Area = 64 ft^2 + (1/2 × 32 ft × 16 ft) = 64 ft^2 + (16 ft × 16 ft) = 64 ft^2 + 256 ft^2 = 320 ft^2
Therefore, the correct answer is:
320 ft.²