To rearrange the surface area equation \( S = \frac{1}{2} lp + B \) for the quantity \( B \), follow these steps:
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Start with the original equation: \[ S = \frac{1}{2} lp + B \]
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To isolate \( B \), subtract \( \frac{1}{2} lp \) from both sides: \[ B = S - \frac{1}{2} lp \]
Thus, the rearranged equation for the quantity of interest \( B \) is: \[ B = S - \frac{1}{2} lp \]