9.9 ft slant
15 ft width
Solve the surface are of the square pyramid
522 ft²
819 ft²
299.25 ft²
148.5 ft²
Choose from the answers presented
Explain
To solve the surface area of a square pyramid, we need to calculate the area of each face and then sum them all up. The formula for the surface area of a square pyramid is:
Surface Area = base area + (0.5 * perimeter * slant height)
First, let's calculate the base area of the square pyramid. Since the base is a square with a width of 15 ft, the area is calculated as:
Base Area = width * width
Base Area = 15 ft * 15 ft
Base Area = 225 ft²
Next, let's calculate the slant height of the pyramid. The slant height is given as 9.9 ft.
Now, we can calculate the surface area of each triangular face. Since the pyramid is a square pyramid, there are 4 triangular faces.
Surface Area of a Triangular Face = (0.5 * perimeter * slant height)
Perimeter of the base square = 4 * width = 4 * 15 ft = 60 ft
Surface Area of each face = (0.5 * 60 ft * 9.9 ft) = 297 ft²
Since there are 4 triangular faces on a square pyramid, the total surface area is:
Total Surface Area = Base Area + 4 * Surface Area of each face
Total Surface Area = 225 ft² + 4 * 297 ft²
Total Surface Area = 225 ft² + 1188 ft²
Total Surface Area = 1413 ft²
Therefore, the closest answer option to the calculated surface area of 1413 ft² is not provided.