Polygon

Polygon

A Polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain or polygonal circuit. The solid plane region, the bounding circuit, or the two together, may be called a polygon.

The segments of a polygonal circuit are called its edges or sides, and the points where two edges meet are the polygon's vertices (singular: vertex) or corners. The interior of a solid polygon is sometimes called its body. An n-gon is a polygon with n sides; for example, a triangle is a 3-gon.

A simple polygon is one which does not intersect itself. Polygons may be characterized by their convexity or type of non-convexity:

• Convex: any line drawn through the polygon (and not tangent to an edge or corner) meets its boundary exactly twice. As a consequence, all its interior angles are less than 180°.
• Non-convex: a line may be found which meets its boundary more than twice, and the interior angle can be greater than 180°.

Types of Polygons

Polygons are primarily classified by the number of sides. Polygons with three through twenty and higher numbers of sides have specific names, for example:

• Triangle (more details): A polygon with three sides.
• Quadrilateral (more details): A polygon with four sides.
• Pentagon (more details): A polygon with five sides.
• Hexagon (more details): A polygon with six sides.
• Heptagon (more details): A polygon with seven sides.
• Octagon (more details): A polygon with eight sides.
• Nonagon (more details): A polygon with nine sides.
• Decagon (more details): A polygon with ten sides.

Properties of Polygons

Polygons have several properties, including:

• Interior Angles (more details): The sum of the measures of the interior angles of a polygon with n sides is (n − 2) × 180°.
• Exterior Angles (more details): The sum of the measures of the exterior angles of a polygon is 360°.
• Area (more details): The area of a polygon can be computed in various ways depending on the type of the polygon.

See Also

• Regular Polygon
• Irregular Polygon
• Convex Polygon
• Concave Polygon

References

Polygon Resources
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External Links

• Wikipedia Article on Polygon