Question

The base of a right prism is a regular hexagon with side 4. The height of the prism is 6. Find the lateral area and volume.

Answer 1

(i) The lateral area of the right prism is 144 square units

(ii) The volume of the right prism is 249.42 cubic units.

Explanation:

The lateral area of the right prism is calculated as;

Lateral area = perimeter of the base x height

Given;

a side of the hexagon base, s = 4

height of the prism = 6

perimeter of the hexagon = 6s

Lateral area = (6 x 4) x 6

Lateral area = 144 square units

Volume of the right prism is calculated as;

V = base area x height

base area of a hexagon =
`(3√(3) \ * \ s^2)/(2)`

Volume of the right prism =
`(3√(3) \ * \ s^2)/(2) \ \ * \ \ h\\\\`

`V = (3√(3) \ * \ (4)^2)/(2) \ \ * \ \ 6\\\\V = 249.42 \ cubic \ units`