Question

find the surface area of this triangular prism. be sure to include the correct unit in your answer.

Explanation:

Step1: Calculate area of triangular bases

The triangular base is a right triangle with legs 5 ft and 12 ft. Area of one triangle is $\frac{1}{2} \times 5 \times 12 = 30$ $\text{ft}^2$. For two bases: $2 \times 30 = 60$ $\text{ft}^2$.

Step2: Calculate area of rectangular faces

Find area of each rectangle:

• Face 1: $5 \times 10 = 50$ $\text{ft}^2$
• Face 2: $12 \times 10 = 120$ $\text{ft}^2$
• Face 3: $13 \times 10 = 130$ $\text{ft}^2$

Sum of rectangular areas: $50 + 120 + 130 = 300$ $\text{ft}^2$.

Step3: Total surface area

Add base and rectangular areas: $60 + 300 = 360$ $\text{ft}^2$.

Answer:

360 $\text{ft}^2$