|- |bgcolor=#e7dcc3|Edges and vertices||5 |- |bgcolor=#e7dcc3|Schläfli symbol||{5} |- |bgcolor=#e7dcc3|Coxeter–Dynkin diagram||



In geometry, a pentagon is any five-sided polygon. A pentagon may be simple or self-intersecting. The internal angles in a simple pentagon total 540°.
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In geometry, a pentagon is any five-sided polygon. A pentagon may be simple or self-intersecting. The internal angles in a simple pentagon total 540°.
Regular pentagons
The term pentagon is commonly used to mean a regular convex pentagon, where all sides are equal and all interior angles are equal (to 108°). Its Schläfli symbol is {5}. The chords of this pentagon are in golden ratio to its sides.
The area of a regular convex pentagon with side length t is given by
- Draw a circle in which to inscribe the pentagon and mark the center point O. (This is the green circle in the diagram to the right).
- Choose a point A on the circle that will serve as one vertex of the pentagon. Draw a line through O and A.
- Construct a line perpendicular to the line OA passing through O. Mark its intersection with one side of the circle as the point B.
- Construct the point C as the midpoint of O and B.
- Draw a circle centered at C through the point A. Mark its intersection with the line OB (inside the original circle) as the point D.
- Draw a circle centered at A through the point D. Mark its intersections with the original (green) circle as the points E and F.
- Draw a circle centered at E through the point A. Mark its other intersection with the original circle as the point G.
- Draw a circle centered at F through the point A. Mark its other intersection with the original circle as the point H.
- Construct the regular pentagon AEGHF.
A pentagram or pentangle is a regular star pentagon. Its Schläfli symbol is {5/2}. Its sides form the diagonals of a regular convex pentagon - in this arrangement the sides of the two pentagons are in the golden ratio.
When a regular pentagon is inscribed in a circle with radius R, its edge length t is given by the expression
Construction
A regular pentagon is constructible using a compass and straightedge, either by inscribing one in a given circle or constructing one on a given edge. This process was described by Euclid in his Elements circa 300 BC.
One method to construct a regular pentagon in a given circle is as follows:

An alternative method is this:
























