For the following question, find the surface area of the regular pyramid shown to the nearest whole number.
A pyramid with a square base is shown. The sides of the square base measure 4 feet. A dashed line which is labeled 7 feet extends from the middle of a side of the base along a triangular surface to the vertex at the top of the pyramid.
(1 point)
Responses
72 ft2
72 ft 2
128 ft2
128 ft 2
56 ft2
56 ft 2
22 ft2
22 ft 2
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To find the surface area of the regular pyramid, we need to calculate the areas of all the triangular faces and add them up with the area of the square base.
The area of the square base is calculated by multiplying the length of one side by itself: 4 ft * 4 ft = 16 ft^2.
The area of each triangular face is calculated by multiplying half of the base (which is the length of one side of the square base) by the height. In this case, the base is 4 ft and the height is 7 ft, so the area of each triangular face is (4 ft * 7 ft) / 2 = 14 ft^2.
Since there are 4 triangular faces in a regular pyramid, the total area of the triangular faces is 4 * 14 ft^2 = 56 ft^2.
Adding the area of the square base and the area of the triangular faces, we get 16 ft^2 + 56 ft^2 = 72 ft^2.
Therefore, the surface area of the regular pyramid is 72 ft^2.