Editing Heptagon (section)

===Area===
The area (''A'') of a regular heptagon of side length ''a'' is given by:

:<math>A = \frac{7}{4}a^2 \cot \frac{\pi}{7} \simeq 3.634 a^2.</math>

This can be seen by subdividing the unit-sided heptagon into seven triangular "pie slices" with [[Vertex (geometry)|vertices]] at the center and at the heptagon's vertices, and then halving each triangle using the [[apothem]] as the common side. The apothem is half the [[cotangent]] of <math>\pi/7, </math> and the area of each of the 14 small triangles is one-fourth of the apothem.

The area of a regular heptagon [[cyclic polygon|inscribed]] in a circle of [[radius]] ''R''  is <math>\tfrac{7R^2}{2}\sin\tfrac{2\pi}{7}, </math> while the area of the circle itself is <math>\pi R^2;</math> thus the regular heptagon fills approximately 0.8710 of its circumscribed circle.