Question

Please help me with this geometry question

Answer 1

`180+18√(3)\ in^2.`

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

`A_(base)=(a^2√(3))/(4),`

where a is the length of the side of equilateral triangle. In your case, a=6 inches. Thus,

`A_(base)=(6^2\cdot√(3))/(4)=9√(3)\ in^2.`

The area of side rectangle is

`A_(side)=ah,`

where h is the height of the rectangle. In your case, h=10 inches. Thus,

`A_(side)=6\cdot 10=60\ in^2.`

Hence, the surface area is

`SA=2\cdot 9√(3)+3\cdot 60=180+18√(3)\ in^2.`