What is the surface area of a square pyramid if the base edge = 68 in and the slant height = 125 in

Answer 1

To find the surface area of a square pyramid, we need to calculate the area of the base and the area of the four triangles that make up the lateral faces.

1. Calculate the area of the base:
The base of the pyramid is a square, so the area is equal to the square of the length of one side. In this case, the base edge is 68 inches, so the area of the base is 68^2 = 4624 square inches.

2. Calculate the area of the lateral faces:
Each lateral face of the pyramid is an isosceles triangle. The slant height is given as 125 inches. To calculate the base of the triangle (which is equal to the side length of the square base), we can use the Pythagorean theorem:
(base)^2 = (slant height)^2 - (height)^2
(base)^2 = 125^2 - 68^2
(base)^2 = 15625 - 4624
(base)^2 = 11001
base = √11001 ≈ 104.83 inches

Now we can calculate the area of one triangle:
Area of a triangle = (base * height) / 2
Area of one triangle = (104.83 * 68) / 2 = 3561.22 square inches

Since the pyramid has four identical triangular faces, the total area of the lateral faces is 4 * 3561.22 = 14244.88 square inches.

3. Calculate the total surface area:
The total surface area is the sum of the area of the base and the area of the lateral faces:
Total surface area = area of base + area of lateral faces
Total surface area = 4624 + 14244.88 = 18868.88 square inches

Therefore, the surface area of the square pyramid is approximately 18868.88 square inches.