Solve for the surface area of the square pyramid. (1 point) Responses 819 ft.2 819 ft. squared 299.25 ft.2 299.25 ft. squared 148.5 ft.2 148.5 ft. squared 522 ft.2
To solve for the surface area of a square pyramid, you need to calculate the area of the base and the area of the four triangular faces.
Given information:
Base side length = 9 ft
Slant height of the pyramid = 17 ft
1. Area of the base:
Since the base is a square, its area is calculated as side length squared.
Base area = 9 ft * 9 ft = 81 ft^2
2. Area of each triangular face:
Since the base is a square, the triangle formed by a side of the base and the slant height of the pyramid is a right triangle. The area of that triangle can be calculated using the formula for the area of a triangle.
Area of each triangle = (0.5 * base length * height)
Area of each triangle = (0.5 * 9 ft * 17 ft) = 76.5 ft^2
3. Total surface area of the pyramid:
Since a square pyramid has 1 base and 4 triangular faces:
Total surface area = Base area + 4 * Triangle area
Total surface area = 81 ft^2 + 4 * 76.5 ft^2
Total surface area = 81 ft^2 + 306 ft^2
Total surface area = 387 ft^2
Therefore, the surface area of the square pyramid is 387 ft^2.