To find the surface area of a square pyramid, we need to calculate the area of the base and the area of the four triangular faces and then add them together.
First, let's find the area of the base. Since the pyramid is a square pyramid, all sides of the base are equal. The formula for the area of a square is side squared.
The side length of the base is given as 15.9 feet. So the area of the base is:
Area_base = 15.9^2 = 252.81 square feet
Next, we need to find the area of the four triangular faces. The formula for the area of a triangle is 1/2 * base * height. In a square pyramid, the base of the triangle is equal to the side length of the base of the pyramid, and the height of each triangular face is the slant height of the pyramid.
The slant height of the pyramid is the hypotenuse of a right triangle with one leg being half the side length of the base (7.95 feet) and the other leg being the height of the pyramid.
Using the Pythagorean theorem, we can calculate the height of the pyramid:
height^2 = slant height^2 - (1/2 * base)^2
height^2 = 15.9^2 - 7.95^2
height^2 = 252.81 - 63.2025
height^2 = 189.6075
height = √189.6075
height ≈ 13.77 feet
Now, we can find the area of each triangular face:
Area_triangular face = 1/2 * 15.9 * 13.77 = 109.42275 square feet
Since there are four triangular faces, the total area of all the triangular faces is:
Total area_triangular faces = 4 * 109.42275 = 437.691 square feet
Finally, we can find the total surface area of the pyramid by adding the area of the base and the area of the four triangular faces:
Total surface area = Area_base + Total area_triangular faces
Total surface area = 252.81 + 437.691
Total surface area = 690.501 square feet
Therefore, the surface area of the square pyramid is 690.501 square feet.
Solve for the surface area of the square pyramid fifteen feet nine point nine feet
1 answer
1 answer