find the surface area of the pyramid
15in
18in
To find the surface area of a pyramid, you need to know the base area and the lateral surface area.
1. Base Area: Since the base of the pyramid is a square, the area of the base is equal to one side squared. Given that one side of the base is 15 inches, the base area is 15in * 15in = 225in^2.
2. Lateral Surface Area: To find the lateral surface area of the pyramid, you need to calculate the area of each triangle face of the pyramid and then sum them up.
Each face of the pyramid is a triangle with a base that is one side of the square base (15in) and height that is the slant height of the pyramid.
Let's calculate the slant height (l) of the pyramid using the Pythagorean theorem:
l^2 = (1/2 * base)^2 + height^2
l^2 = (1/2 * 15in)^2 + 18in^2
l^2 = 112.5in^2 + 18in^2
l^2 = 130.5in^2
l ≈ 11.42in
Now that we have the slant height, we can calculate the lateral surface area:
Lateral Surface Area (LSA) = 1/2 * base * slant height * number of faces
LSA = 1/2 * 15in * 11.42in * 4 = 342.6in^2
3. Total Surface Area:
Total Surface Area = Base Area + Lateral Surface Area
Total Surface Area = 225in^2 + 342.6in^2 = 567.6in^2
Therefore, the surface area of the pyramid is 567.6 square inches.