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Question

# The United State Department of Defense is located in a building called the Pentagon because it is in the shape of a regular pentagon. Known as "the largest office building in the world," its exterior edges measure 921 feet. Find the area of land enclosed by the outer walls of the Pentagon building.

Solutions

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The area of a regular pentagon with side length $s$ is calculated by the formula:

$\boxed {A=\dfrac {1}{4} \cdot \sqrt {5(5+2\cdot \sqrt {5})}\cdot s^2}$

The area of the united states pentagon:

\begin{align*} A&=\dfrac {1}{4} \cdot \sqrt {5(5+2\cdot \sqrt {5})}\cdot 921^2 \\ &\boxed {\color{#c34632} \approx 1,459,379 \text { ~ft}^2} \end{align*}

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