9.9 ft
15 ft
Solve the surface are of the square pyramid
522 ft²
819 ft²
299.25 ft²
148.5 ft²
Choose from the answers presented
Explain
its 522 ft
To solve for the surface area of a square pyramid, we need to calculate the area of the base and the area of the four triangular faces.
The area of the base is calculated by finding the area of a square with a side length of 9.9 ft:
Base area = (side length)^2 = 9.9 ft * 9.9 ft = 98.01 ft²
The area of each triangular face can be calculated using the formula:
Triangle area = 0.5 * base * height
The height of the pyramid can be calculated using the Pythagorean theorem:
height = √(15^2 - (9.9/2)^2) = √(225 - 48.01) = √176.99 ≈ 13.31 ft
Now we can calculate the area of each triangular face:
Triangle area = 0.5 * 9.9 ft * 13.31 ft = 66.035 ft²
Since the pyramid has 4 triangular faces, the total surface area is:
Total surface area = Base area + 4 * Triangle area = 98.01 ft² + 4 * 66.035 ft² = 98.01 ft² + 264.14 ft² = 362.15 ft²
Therefore, the closest answer from the given options is 299.25 ft².