Question

Help ASAP worth 20 points. A special box designed to hold an antique artifact is shaped

like a triangular prism. The surface area of the box is
421.2 square inches. The height of the base triangle is 7.8 inches
and each side of the base triangle is 9 inches long. What is the
height of box?

Answer 1

The height of the box is
`13\ in`

Explanation:

we know that

The surface area of the triangular prism is equal to

`SA=2B+PH`

where

B is the area of the base

P is the perimeter of the base

H is the height of the box

Find the area of the base B

`B=(1)/(2)bh`

we have

`b=9\ in`

`h=7.8\ in`

substitute

`B=(1)/(2)(9)(7.8)=35.1\ in^(2)`

Find the perimeter of the base

`P=3b=3*9=27\ in`

Find the height of the box

`SA=B+PH`

we have

`SA=421.2\ in^(2)`

`B=35.1\ in^(2)`

`P=27\ in`

substitute and solve for H

`421.2=2(35.1)+27H`

`27H=351`

`H=351/27=13\ in`