Find the surface area of a square pyramid with side length 1 mi and slant height 4 mi.

Answer 1

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

The lateral surface area of a square pyramid can be calculated using the formula:
Lateral surface area = 0.5 * perimeter of base * slant height

Since the base of the pyramid is a square with side length 1 mi, the perimeter of the base is 4 * 1 = 4 mi.

Plugging in the values:
Lateral surface area = 0.5 * 4 * 4 = 8 mi^2

Now, let's calculate the area of the square base:
Base area = side length^2 = 1^2 = 1 mi^2

Finally, we can calculate the total surface area of the pyramid by adding the lateral surface area and the base area:
Surface area = 8 + 1 = 9 mi^2

Therefore, the surface area of the square pyramid is 9 square miles.