15ft 9.9ft solve for the surface area of a square pyraimid
To find the surface area of a square pyramid, we need to calculate the area of the square base and the area of the four triangular faces.
Given that the base of the square pyramid is 15 feet by 15 feet and the height of the pyramid is 9.9 feet, we can calculate the surface area as follows:
1. Calculate the area of the square base:
Area of square base = side length^2
Area of square base = 15ft x 15ft = 225ft^2
2. Calculate the area of each triangular face:
The triangular face is an isosceles triangle, so we need to calculate the height of the triangle using the Pythagorean theorem:
h^2 = (0.5 x 15ft)^2 + (9.9ft)^2
h^2 = 112.275
h ≈ 10.6ft
Area of each triangular face = 0.5 x base x height
Area of each triangular face = 0.5 x 15ft x 10.6ft = 79.5ft^2
3. Calculate the total surface area of the square pyramid:
Total surface area = 4 x area of each triangular face + area of the square base
Total surface area = 4 x 79.5ft^2 + 225ft^2
Total surface area = 318ft^2 + 225ft^2
Total surface area = 543ft^2
Therefore, the surface area of the square pyramid is 543 square feet.