Question

Amanda has a shipping box in the shape of a triangular prism. It is 9 inches tall with a triangular base that is 3 inches by 2 inches. What is the volume of this shipping box?

Answer 1

Answer:

The volume of the shipping box is $V=27\ in^3$

Step-by-step explanation:

see the attached figure to better understand the problem

The volume of the triangular prism is equal to

$V=BH$

where

B is the area of the triangular base

H is the height of the prism

In this problem we have

$H=9\ in$

Find the area of the triangular base B

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

we have

$b=3\ in\\h=2\ in$

substitute

$B=\frac{1}{2}(3)(2)=3\ in^2$

Find the volume of the triangular prism

$V=BH$

we have

$B=3\ in^2$

$H=9\ in$

substitute

$V=(3)(9)=27\ in^3$