# Heptagon

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A heptagon is a plane figure with seven sides and seven angles. In a regular heptagon, in which all sides and all angles are equal, the sides meet at an angle of approximately 128.6 degrees. Its Schläfli symbol is {7}. The area of a regular heptagon of side length a is given by

[itex]A = \frac{7}{4}a^2 \cot \frac{\pi}{7} \simeq 3.63391 a^2.[itex]

A regular heptagon is not constructible with straightedge and compass.

The United Kingdom currently (2003) has two heptagonal coins, the 50p and 20p pieces. Strictly, the shape of the coins is a curvilinear heptagon: the sides are curved outwards so that the coin will roll smoothly in vending machines.

The heptagon is also sometimes referred to as the septagon, using "sept-" (an elision of septua-, a Latin-derived numerical prefix) for seven, rather than hepta-, a Greek-derived numerical prefix.

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