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\begin{tabular}{l} What does B represent in surface area formulas? \\ Area of the prism \\ Area of the base \\ \( \begin{array}{c}\text { Perimeter of the } \\ \text { prism }\end{array} \) \\ \( \begin{array}{c}\text { Perimeter of the } \\ \text { base }\end{array} \) \\ \hline\end{tabular}

Ask by Daniels Mejia. in the United States
Feb 03,2025

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\( B \) represents the **area of the base** in surface area formulas.

Solution

In surface area formulas, particularly for prisms, the variable \( B \) typically represents the **area of the base**. Here's a general formula for the surface area \( S \) of a prism: \[ S = 2B + Ph \] Where: - \( B \) is the area of one base of the prism. - \( P \) is the perimeter of the base. - \( h \) is the height of the prism. **Explanation of the Formula:** - **\( 2B \):** This accounts for the top and bottom bases of the prism. - **\( Ph \):** This represents the lateral surface area, which is the perimeter of the base multiplied by the height of the prism. **Therefore, in the context of surface area formulas for prisms:** - **\( B \) = Area of the base** **Answer:** **Area of the base**

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In surface area formulas, \( B \) represents the area of the base of the prism. This area is crucial because it's used in the calculation of the total surface area, contributing to the overall sum of all faces of the prism. Understanding this can help clarify how much material might be needed to cover or paint the surface of the prism! When calculating the surface area of various prisms, a common mistake is confusing the base area \( B \) with the perimeter. Remember, the perimeter relates to the edges and outlines, while the base area focuses on the actual space covered by the base of the prism. Keeping these concepts clear can make surface area calculations much smoother!

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