Answer:
The surface area is equal to [tex]203\ m^{2}[/tex]
Step-by-step explanation:
step 1
Find the height of the prism
we know that
The volume of the prism is equal to
[tex]V=Bh[/tex]
where
B is the area of the base of the prism
h is the height of the prism
we have
[tex]V=160\ m^{3}[/tex]
[tex]B=64\ m^{2}[/tex]
substitute in the formula and solve for h
[tex]160=64h[/tex]
[tex]h=160/64=2.5\ m[/tex]
step 2
Find the surface area
The surface area of the prism is equal to
[tex]SA=2B+Ph[/tex]
where
B is the area of the base of the prism
P is the perimeter of the base
h is the height of the prism
we have
[tex]B=64\ m^{2}[/tex]
[tex]P=30\ m[/tex]
[tex]h=2.5\ m[/tex]
substitute in the formula
[tex]SA=2(64)+(30)(2.5)=203\ m^{2}[/tex]
