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)
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Item
◎ 512ft2
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O 128 ft.?
O 256 ft.?
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• 320 ft.?
The surface area of a square pyramid is found by adding the area of the base to the sum of the areas of the four triangular faces.
The area of the base is found by multiplying the length of one side (base edge) by itself: 8 ft * 8 ft = 64 ft^2.
The area of each triangular face can be found by multiplying half the perimeter of the base by the slant height: (8 ft + 8 ft + 8 ft + 8 ft)/2 * 16 ft = 32 ft * 16 ft = 512 ft^2.
Since there are four triangular faces, the total area of all four faces is 512 ft^2 * 4 = 2048 ft^2.
Adding the area of the base (64 ft^2) to the sum of the areas of the four triangular faces (2048 ft^2) gives a total surface area of 64 ft^2 + 2048 ft^2 = 2112 ft^2.
Therefore, the correct answer is not among the given options.