Answer:
The surface area of the prism is [tex](18\sqrt{3}+180)\ in^{2}[/tex]
Step-by-step explanation:
we know that
The surface area of the triangular prism is equal to
[tex]SA=2B+PH[/tex]
where
B is the area of the triangular base
P is the perimeter of the triangular base
H is the height of the prism
Find the area of the base B
Applying the law of sines to find the area of a equilateral triangle
[tex]B=\frac{1}{2}b^{2} sin(60\°)[/tex]
we have
[tex]b=6\ in[/tex]
[tex]sin(60\°)=\sqrt{3}/2[/tex]
substitute
[tex]B=\frac{1}{2}6^{2}(\sqrt{3}/2)[/tex]
[tex]B=9\sqrt{3}\ in^{2}[/tex]
Find the perimeter P
[tex]P=3*6=18\ in[/tex]
we have
[tex]H=10\ in[/tex]
substitute the values
[tex]SA=2(9\sqrt{3})+(18)(10)=(18\sqrt{3}+180)\ in^{2}[/tex]
