Question

A square pyramid. The square base has side lengths of 6 inches. The 4 triangular sides have a base of 6 inches and height of 9 inches.

Complete the sentences.


The area of the pyramid’s base is in.2.

The pyramid has lateral faces.

The surface area of each lateral face is in.2.

The total surface area is 144 in.2.

Answer 1

The area of the pyramid’s base is 36 in².

The pyramid has 4 lateral faces.

The surface area of each lateral face is 27 in².

Explanation:

"Lateral" means side, so the lateral faces are triangles.

The base is the bottom, which is a square.

To calculate the area of the base, use the formula for area of a square.

`A_(base) = s^(2)`

`A_(base) = (6 in)^(2)`

`A_(base) = 36 in^(2)`

To calculate the area of a lateral face, find the area of a triangle.

`A_(lateral) = (bh)/(2)`

`A_(lateral) = ((6 in)(9 in))/(2)`

`A_(lateral) = (54 in^(2))/(2)`

`A_(lateral) = 27 in^(2)`

In a pyramid, the number of lateral faces is the same as the number of sides in the base. The square base as 4 sides, so there are 4 lateral faces.