\begin{tabular}{|l}\begin{tabular}{|l} (a) Find the following side lengths for the net. \ $$ A=3[\mathrm{~cm} $$ \ $$ B=8 \mathrm{~cm} $$ \ $$ C=4 \mathrm{~cm} $$ \ D $$ =5 \mathrm{~cm} $$\end{tabular} \ (b) Use the net to find the surface area of the prism. \ $$ \square \mathrm{cm}^{2} $$\end{tabular}

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**(a)**  
We interpret the net as that of a triangular prism whose bases are right triangles with legs  
$$
A=3\text{ cm}\quad\text{and}\quad C=4\text{ cm},
$$
and hypotenuse  
$$
D=5\text{ cm}.
$$
The “length” of the prism (the distance between the two triangular bases) is  
$$
B=8\text{ cm}.
$$

**(b)**  
A triangular prism has two triangular bases and three lateral rectangular faces. Its total surface area can be computed as

$$
\text{SA} = 2(\text{Area of one triangular base}) + (\text{Perimeter of the base})(\text{Length of the prism}).
$$

1. **Area of the triangular base:**  
   For a right triangle with legs $$3\text{ cm}$$ and $$4\text{ cm}$$,
   $$
   \text{Area} = \frac{1}{2}(3)(4) = 6\text{ cm}^2.
   $$

2. **Perimeter of the triangular base:**  
   $$
   P = 3 + 4 + 5 = 12\text{ cm}.
   $$

3. **Lateral surface area:**  
   The three lateral faces form a rectangle when “unfolded,” with area
   $$
   \text{Lateral Area} = P \times B = 12 \times 8 = 96\text{ cm}^2.
   $$

4. **Total Surface Area:**  
   $$
   \text{SA} = 2(6) + 96 = 12 + 96 = 108\text{ cm}^2.
   $$

Thus, the surface area of the prism is  
$$
108\text{ cm}^2.
$$
**(a)** The net represents a triangular prism with triangular bases having sides $$ A=3\text{ cm} $$, $$ C=4\text{ cm} $$, and hypotenuse $$ D=5\text{ cm} $$. The length between the bases is $$ B=8\text{ cm} $$. **(b)** The surface area of the prism is $$ 108\text{ cm}^2. $$

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