Using a net to find the surface area of a triangular prism (a) Find the following side lengths for the net. \[ \begin{array}{l}\text { A }=15 \mathrm{yd} \\ B=2 \mathrm{yd} \\ C=8 \mathrm{yd} \\ D=17] \mathrm{yd} \\ \text { (b) Use the net to find the surface area of the prism. } \\ \square \text { yd }{ }^{2}\end{array} \]

**Step 1. Determine the dimensions.** We interpret the given quantities as follows: - The triangular base has side lengths \[ a=15\text{ yd},\quad b=8\text{ yd},\quad c=17\text{ yd}. \] (Notice that \(15\), \(8\), and \(17\) make a well‐known Pythagorean triple so that the triangle is right with legs \(15\) and \(8\).) - The height (or “length”) of the prism is \[ h=2\text{ yd}. \] A net of a triangular prism shows two triangular bases and three adjoining rectangles. For the net, the side lengths are: - The triangle’s sides are \(15\), \(8\), and \(17\) yd. - The three rectangular faces have one side equal to one of these triangle sides and the other side equal to the prism’s height \(2\) yd. Their dimensions are: - Rectangle 1: \(15\) yd by \(2\) yd. - Rectangle 2: \(8\) yd by \(2\) yd. - Rectangle 3: \(17\) yd by \(2\) yd. **Step 2. Compute the area of the triangular bases.** Because the triangle is right (the legs \(15\) and \(8\) are perpendicular), its area is \[ A_{\triangle}=\frac{1}{2}\times 15 \times 8=60\text{ yd}^2. \] There are two such triangles, so their combined area is \[ 2\times 60=120\text{ yd}^2. \] **Step 3. Compute the lateral (rectangular) areas.** The three lateral faces are rectangles whose areas are given by \[ \begin{aligned} \text{Area}_1 &= 15\times 2 = 30\text{ yd}^2,\\[1mm] \text{Area}_2 &= 8\times 2 = 16\text{ yd}^2,\\[1mm] \text{Area}_3 &= 17\times 2 = 34\text{ yd}^2. \end{aligned} \] Their total lateral area is \[ 30+16+34=80\text{ yd}^2. \] **Step 4. Find the total surface area.** Adding the areas of the two bases and the three lateral faces gives \[ \text{Surface Area}=120+80=200\text{ yd}^2. \] Thus, the surface area of the prism is \[ 200\text{ yd}^2. \]