Find the surface area of a square pyramid with side length 4 in and slant height 4 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 triangular faces.

The area of the base of the square pyramid is:
Base area = side length^2
Base area = 4^2
Base area = 16 square inches

Next, we need to calculate the area of the four triangular faces. Each triangular face is an isosceles triangle with base equal to side length of the square base and two equal sides equal to the slant height.

The area of one triangular face is:
Face area = 0.5 * base * height
Face area = 0.5 * 4 * 4
Face area = 8 square inches

Since there are 4 triangular faces, the total area of the four triangular faces is:
Total face area = 4 * Face area
Total face area = 4 * 8
Total face area = 32 square inches

Finally, the surface area of the square pyramid is:
Surface area = Base area + Total face area
Surface area = 16 + 32
Surface area = 48 square inches

Therefore, the surface area of the square pyramid is 48 square inches.