Question

The surface area of a regular pyramid with a square base which has a slant height of five units and base side lengths of nine units is:

Answer 1

171 sq units.

Explanation:

Since you don't specify you want a the side surface area only, we'll calculate both.

First, the base...

We have a square with a side of 9 units.

Area of the base is then 9 x 9 = 81 sq units.

For the sides, we have 4 triangles with a base of 9 and a height of 5 units.

The area of a triangle is calculated with A = (b * h)/2

So, each of the sides of the pyramid has an area of:

A = (9 * 5) / 2 = 22.5 sq units

There are four sides, so total lateral area: 4 * 22.5 = 90 sq units.

Total area: 81 + 90 = 171 sq units.