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\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}

Ask by Cross Luna. in the United States
Mar 15,2025

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**(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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Bonus Knowledge

To find the side lengths of the net, you can simply use the values provided: A = 3 cm, B = 8 cm, C = 4 cm, and D = 5 cm. For each side, just ensure they are represented accurately in your net, which consists of rectangles corresponding to the sides of the prism. Once you've laid out your net, calculating the surface area can be quite exciting! For a rectangular prism, the formula for surface area is \( 2(lw + lh + wh) \), where l is length, w is width, and h is height. Here, you can interpret A, B, C, and D as the dimensions of the prism. After applying these values, sum up all areas and multiply by 2 to find the total surface area in square centimeters! Happy calculating!

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