Question
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(a) Find the following side lengths for the net. \( \begin{array}{l}A=15 \mathrm{~mm} \\ B=17 \mathrm{~mm} \\ C=4 \mathrm{~mm} \\ D=81 \mathrm{~mm} \\ \text { (b) Use the net to find the surface area of the prism. } \\ \text { ( }\end{array} \).

Ask by Sherman King. in the United States
Mar 14,2025

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The surface area of the prism is \(12\sqrt{21} + 2916\) square millimeters.

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Beyond the Answer

To tackle your problem, let’s visualize the prism. The dimensions given correspond to the edges of the rectangular base and the height. Typically, for a rectangular prism, the net consists of two rectangular bases and four rectangular lateral faces. To find the surface area, you can use the formula: Surface Area = 2 * (length * width) + perimeter of the base * height. Substituting your values (A, B, C, D) appropriately based on which represents width, length, and height will yield the total surface area. For the specific side lengths, you might be looking at possibly \( A = \text{width} \), \( B = \text{length} \), \( C = \text{height} \), leading to easier calculations. Remember, always double-check which dimensions correspond to the sides! This common mistake often leads to confusion in calculations.

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