Question

# A regular heptagon (7 sides) has perimeter 126 and area A. Express the apothem a of the heptagon algebraically in terms of the area A.

Solution

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Determine the apothem of the regular heptagon.

\begin{align*} A &= \dfrac{1}{2}ap && \text{Write the equation}\\ A &= \dfrac{1}{2}a(126) && \text{Substitute the values}\\ A &= \dfrac{1}{2}(126a) && \text{Multiply the values}\\ A &= 63a && \text{Multiply the values}\\ \dfrac{A}{63} &= \dfrac{63a}{63} && \text{Divide both sides by 63}\\ \dfrac{A}{63} &= a && \text{Simplify} \end{align*}

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