Question

A certain hexagonal prism has a volume of 160 cubic meters. Its base has a perimeter of 30 meters and an area of 64 square meters. What is the surface area in square meters of the hexagonal prism??

Answer 1

The surface area is equal to
`203\ m^(2)`

Explanation:

step 1

Find the height of the prism

we know that

The volume of the prism is equal to

`V=Bh`

where

B is the area of the base of the prism

h is the height of the prism

we have

`V=160\ m^(3)`

`B=64\ m^(2)`

substitute in the formula and solve for h

`160=64h`

`h=160/64=2.5\ m`

step 2

Find the surface area

The surface area of the prism is equal to

`SA=2B+Ph`

where

B is the area of the base of the prism

P is the perimeter of the base

h is the height of the prism

we have

`B=64\ m^(2)`

`P=30\ m`

`h=2.5\ m`

substitute in the formula

`SA=2(64)+(30)(2.5)=203\ m^(2)`