Answer:
[tex]180+18\sqrt{3}\ in^2.[/tex]
Step-by-step explanation:
The surface area of right triangular prism is the sum of area of two base triangles and 3 area of side rectangles.
The area of base triangle is
[tex]A_{base}=\dfrac{a^2\sqrt{3}}{4},[/tex]
where a is the length of the side of equilateral triangle. In your case, a=6 inches. Thus,
[tex]A_{base}=\dfrac{6^2\cdot\sqrt{3}}{4}=9\sqrt{3}\ in^2.[/tex]
The area of side rectangle is
[tex]A_{side}=ah,[/tex]
where h is the height of the rectangle. In your case, h=10 inches. Thus,
[tex]A_{side}=6\cdot 10=60\ in^2.[/tex]
Hence, the surface area is
[tex]SA=2\cdot 9\sqrt{3}+3\cdot 60=180+18\sqrt{3}\ in^2.[/tex]
