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
To find the surface area of the regular pyramid, we need to find the area of the base and the area of the four triangular faces.
Area of base = 4 ft x 4 ft = 16 ft²
Area of one triangle = (1/2)base x height = (1/2)(4 ft)(7 ft) = 14 ft²
Total area of all four triangles = 4 x 14 ft² = 56 ft²
Total surface area of the pyramid = Area of base + Total area of all four triangles
Total surface area = 16 ft² + 56 ft²
Total surface area = 72 ft²
Therefore, the surface area of the regular pyramid is 72 ft².