Question

total surface area = ?
12 in
9 in
15 in
2 in

Explanation:

Step1: Identify shape components

This is a net of a triangular prism, consisting of 2 congruent right triangles and 3 rectangles.

Step2: Calculate triangle area

Area of 1 right triangle: $\frac{1}{2} \times 9 \times 12 = 54$ square inches.
Total area for 2 triangles: $2 \times 54 = 108$ square inches.

Step3: Calculate rectangle areas

Area of 1st rectangle: $9 \times 2 = 18$ square inches.
Area of 2nd rectangle: $12 \times 2 = 24$ square inches.
Area of 3rd rectangle: $15 \times 2 = 30$ square inches.

Step4: Sum all areas

Total surface area = sum of triangle areas + sum of rectangle areas
$\text{Total Surface Area} = 108 + 18 + 24 + 30$

Answer:

180 square inches