Use the image to answer the question.
Solve for the surface area of the square pyramid.
(1 point)
299.25 ft.2
522 ft.2
148.5 ft.2
819 ft.2
To solve for the surface area of the square pyramid, we need to calculate the area of the base and the area of the four triangular faces.
Given that each side of the base square measures 15 feet and the slant height is 20 feet, we can find the area of the base by squaring the side length:
Base area = 15 ft x 15 ft = 225 ft^2
Now, to calculate the area of one triangular face, we can use the formula:
Area of 1 triangular face = 0.5 x base x height
= 0.5 x 15 ft x 20 ft
= 150 ft^2
Since there are four triangular faces, the total area of the four faces is:
4 x 150 ft^2 = 600 ft^2
Therefore, the total surface area of the square pyramid is the sum of the base area and the area of the four faces:
Total surface area = 225 ft^2 + 600 ft^2 = 825 ft^2
So the surface area of the square pyramid is 825 ft^2.
Given the options provided, the closest answer is 819 ft^2.