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

Answer:

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

Step-by-step 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

$SA=2B+PH$

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

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

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

$H=58.36\ m$