Question

(a) find the following side lengths for the net.
a = 8 ft
b = 3 ft
c = 4 ft
d = 5 ft
(b) use the net to find the surface area of the prism.
\\(\square\\) \\(\text{ft}^2\\)

Explanation:

Step1: Identify the prism type

The prism is a triangular prism. The triangular base has legs 3 ft and 4 ft (right triangle), hypotenuse 5 ft. The length of the prism (A) is 8 ft.

Step2: Recall surface area formula for triangular prism

Surface Area \( SA = 2 \times \text{Area of triangular base} + \text{Perimeter of triangular base} \times \text{length of prism} \)

Step3: Calculate area of triangular base

Area of triangle \( = \frac{1}{2} \times 3 \times 4 = 6 \, \text{ft}^2 \)

Step4: Calculate perimeter of triangular base

Perimeter \( = 3 + 4 + 5 = 12 \, \text{ft} \)

Step5: Calculate surface area

\( SA = 2 \times 6 + 12 \times 8 = 12 + 96 = 108 \, \text{ft}^2 \)

Answer:

108