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.
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
1 answer
1 answer