Question

what is the surface area of this triangular prism?
10 in.
8 in.
10 in.
12 in.
15 in.
____ square inches

Explanation:

Step1: Find area of 2 triangular bases

The area of one triangle is $\frac{1}{2} \times \text{base} \times \text{height}$, so for two triangles:
$2 \times \frac{1}{2} \times 12 \times 8 = 96$ square inches

Step2: Find area of 3 rectangular faces

Calculate area of each rectangle and sum:
$12 \times 15 + 10 \times 15 + 10 \times 15 = 180 + 150 + 150 = 480$ square inches

Step3: Sum all areas for total surface area

Add the area of the triangular bases and rectangular faces:
$96 + 480 = 576$

Answer:

576 square inches