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

Answer:

The height of the box is $13\ in$

Step-by-step 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

$B=\frac{1}{2}bh$

we have

$b=9\ in$

$h=7.8\ in$

substitute

$B=\frac{1}{2}(9)(7.8)=35.1\ in^{2}$

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

$421.2=2(35.1)+27H$

$27H=351$

$H=351/27=13\ in$