Question

The base of a hexagonal prism has an apothem measuring 10 inches and an area of 346.41 square inches. The prism is 12 inches tall. What is the approximate lateral area of the prism? Round to the nearest whole number.

Answer 1

831 In^3

Explanation:

Edge 2020

Answer 2

The approximate lateral area of the prism is
`831\ in^{2`

Explanation:

we know that

The lateral area of the prism is equal to

`LA=PH`

where

P is the perimeter of the base of the prism

H is the height of the prism

Find the perimeter of the hexagonal base

Remember that the area of the hexagonal base is equal to

`A=(1)/(2) P(a)`

where

P is the perimeter

a is the apothem

we have

`A=346.41\ in^(2)`

`a=10\ in`

substitute and solve for P

`346.41=(1)/(2) P(10)`

`P=346.41/5=69.282\ in`

Find the lateral area

`LA=PH`

we have

`P=69.282\ in`

`H=12\ in`

substitute the values

`LA=(69.282)(12)=831\ in^{2`