Heptagon
In geometry, a heptagon is a seven-sided polygon or 7-gon.
The heptagon is also occasionally referred to as the septagon, using "sept-" (an elision of septua-, a Latin-derived numerical prefix, rather than hepta-, a Greek-derived numerical prefix) together with the Greek suffix "-agon" meaning angle.
Regular heptagon
A regular heptagon, in which all sides and all angles are equal, has internal angles of 5π/7 radians (128.5714286 degrees). Its Schläfli symbol is {7}.
Area
The area (A) of a regular heptagon of side length a is given by:
This can be seen by subdividing the unit-sided heptagon into seven triangular "pie slices" with 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 
and the area of each of the 14 small triangles is one-fourth of the apothem.
The exact algebraic expression, starting from the polynomial x3 + x2 − 2x − 1 (one of whose roots is 
) is given by:
where 
is the imaginary unit.
