Question

Find the height of a rectangular prism if the surface area is 3,834 square meters and the length of the base is 14.2 meters and the width of the base is 15 meters

Answer 1

The height of the rectangular prism is
`58.36\ m`

Explanation:

we know that

The surface area of the rectangular prism is equal to

`SA=2B+PH`

where

B is the area of the rectangular base

P is the perimeter of the rectangular base

H is the height of the prism

Find the area of the base B

`B=14.2*15=213\ m^(2)`

Find the perimeter of the base P

`P=2(14.2+15)=58.4\ m`

we have

`SA=3,834\ m^(2)`

substitute and solve for H

`SA=2B+PH`

`3,834=2(213)+(58.4)H`

`3,834=426+(58.4)H`

`H=(3,834-426)/(58.4)`

`H=58.36\ m`