Question

Please help me with this geometry question

Answer 1

Answer:

$180+18\sqrt{3}\ in^2.$

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

$A_{base}=\dfrac{a^2\sqrt{3}}{4},$

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

$A_{base}=\dfrac{6^2\cdot\sqrt{3}}{4}=9\sqrt{3}\ in^2.$

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

$SA=2\cdot 9\sqrt{3}+3\cdot 60=180+18\sqrt{3}\ in^2.$