9.9ft 15ft
Solve for the surface area of the square pyramid
522ft
819ft
299.25 ft
148.5 fr
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.
1. Area of the base:
Given that the base is a square, we can calculate the area by squaring one of the sides.
Base Area = (Side)^2 = (9.9ft)^2 = 98.01ft^2
2. Area of the triangular faces:
Since the pyramid is a square pyramid, the triangular faces are all identical. Each triangular face is an isosceles triangle with a base length equal to the side length of the square base (9.9ft) and a height equal to the slant height of the pyramid (15ft).
Area of each triangular face = 0.5 * Base * Height
Area of each triangular face = 0.5 * 9.9ft * 15ft = 74.25ft^2
Total surface area of the pyramid:
Surface Area = Base Area + 4(Triangular Face Area)
Surface Area = 98.01ft^2 + 4(74.25ft^2)
Surface Area = 98.01ft^2 + 297ft^2
Surface Area = 395.01ft^2
Therefore, the surface area of the square pyramid is 395.01ft^2.