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 148.5 ft.2 148.5 ft. squared 819 ft.2 819 ft. squared 522 ft.2
To solve for the surface area of the square pyramid, we need to calculate the area of the base (the square) and the area of the four triangular faces.
Given that the base of the square pyramid has sides measuring 10.5 ft, we can calculate the area of the base:
Area of base = side^2 = 10.5^2 = 110.25 ft^2
Next, we need to calculate the area of the four triangular faces.
Since the base side length is 10.5 ft and the slant height is 9 ft, we can use the formula:
Area of a triangle = 0.5 x base x height
= 0.5 x 10.5 x 9 = 47.25 ft^2
Since there are four triangular faces, the total area of the triangular faces = 4 x 47.25 = 189 ft^2
Finally, the total surface area of the square pyramid is the sum of the base area and the total area of the triangular faces:
Total surface area = base area + total area of triangular faces
= 110.25 + 189
= 299.25 ft^2
Therefore, the surface area of the square pyramid is 299.25 ft^2 or 299.25 ft^2.
So, the correct response is:
299.25 ft.²