Answer:
[tex]\huge\boxed{V=288\ in^3}[/tex]
Step-by-step explanation:
The formula of a volume of a prism:
[tex]V=BH[/tex]
where
B - area of a base
H - height of a prism
In the base we have the trapezoid.
The formula of an area of a trapezoid:
[tex]A=\dfrac{b_1+b_2}{2}\cdot h[/tex]
Where
[tex]b_1,\ b_2[/tex] - bases
[tex]h[/tex] - height of a trapezoid
From the picture we have:
[tex]b_1=16\ in,\ b_2=8\ in,\ h=6\ in[/tex]
Substitute:
[tex]B=\dfrac{16+8}{2}\cdot6=\dfrac{24}{2}\cdot6=12\cdot6=72\ in^2[/tex]
Substitute it and H = 4 in to the formula of a volume of a prism:
[tex]V=(72)(4)=288\ in^3[/tex]
