Solve for surface area of square pyramid with base of 15 and height of 9.9
To find the surface area of a square pyramid, we need to add the area of the base to the area of each of the four triangular faces.
The formula for the surface area of a square pyramid is:
Surface Area = (0.5 * Perimeter of Base * Slant Height) + Base Area
First, let's find the perimeter of the base (15) and then calculate the slant height:
Perimeter of the base = 4 * side length
Perimeter of the base = 4 * 15 = 60
Now, to find the slant height (hypotenuse) of one of the triangular faces, we use the Pythagorean theorem:
slant height^2 = height^2 + (side length/2)^2
slant height^2 = 9.9^2 + (15/2)^2
slant height^2 = 98.01 + 56.25
slant height^2 = 154.26
slant height ≈ 12.42
Now, we can plug the values into the formula to find the surface area:
Surface Area = (0.5 * 60 * 12.42) + 15^2
Surface Area = (30 * 12.42) + 225
Surface Area = 372.6 + 225
Surface Area = 597.6
Therefore, the surface area of the square pyramid is 597.6 square units.