Question

Solve for the surface area of the square pyramid.

Answer 1

To find the surface area of a square pyramid, we need to calculate the area of the base and the lateral faces.

1. Calculate the area of the base:
- Let's say the side length of the base of the square pyramid is 's'.
- The area of the square base is s^2.

2. Calculate the area of each of the four triangular lateral faces:
- The triangle is an isosceles right triangle with legs equal to the slant height (h) and base equal to the side length of the base (s).
- The area of one triangle is (1/2) * base * height = (1/2) * s * h.
- Since there are 4 triangular faces, the total area of the lateral faces is 4 * (1/2) * s * h = 2sh.

3. Add the area of the base and the total area of the lateral faces to find the surface area of the square pyramid:
- Surface Area = Area of base + Area of lateral faces
= s^2 + 2sh
= s^2 + 2s * h
= s(s + 2h)

Therefore, the surface area of a square pyramid is given by the formula: s(s + 2h).