(a) Find the following side lengths for the net. \( A=15 \mathrm{yd} \) \( B=2 \mathrm{yd} \) \( C=8 \mathrm{yd} \) \( D=17 \mid \mathrm{yd} \) (b) Use the net to find the surface area of the prism. \( \square \mathrm{yd}{ }^{2} \)

To solve the problem, we need to find the side lengths for the net and then use those lengths to calculate the surface area of the prism. ### Part (a): Finding the Side Lengths for the Net The given dimensions are: - \( A = 15 \, \text{yd} \) - \( B = 2 \, \text{yd} \) - \( C = 8 \, \text{yd} \) - \( D = 17 \, \text{yd} \) Assuming these dimensions represent the lengths of the edges of a rectangular prism, we can identify the lengths of the sides of the net. For a rectangular prism, the net consists of: - 2 rectangles for the top and bottom (length \( A \) and width \( B \)) - 2 rectangles for the front and back (length \( C \) and height \( D \)) - 2 rectangles for the left and right sides (width \( B \) and height \( D \)) ### Part (b): Finding the Surface Area of the Prism The surface area \( S \) of a rectangular prism can be calculated using the formula: \[ S = 2(AB + AC + BC) \] Where: - \( A \) is the length, - \( B \) is the width, - \( C \) is the height. Substituting the values into the formula: \[ S = 2(15 \cdot 2 + 15 \cdot 8 + 2 \cdot 8) \] Now, let's calculate the individual products: 1. \( 15 \cdot 2 = 30 \) 2. \( 15 \cdot 8 = 120 \) 3. \( 2 \cdot 8 = 16 \) Now, summing these products: \[ 30 + 120 + 16 = 166 \] Finally, multiplying by 2 to find the total surface area: \[ S = 2 \cdot 166 = 332 \, \text{yd}^2 \] Thus, the surface area of the prism is: \[ \boxed{332 \, \text{yd}^2} \]