# Polygons

A polygon is a two dimensional shape formed by connecting three or more line segments at vertices. The term originates from the Greek word "poly" which means "many" and "gon" which means "a closed figure".

A polygon with three sides is a called a triangle. A polygon with four sides is called a quadrilateral. Special cases of quadrilaterals include shapes like trapezoids, rectangle, rhombuses and squares. Other polygons are:

• Pentagon: A five-sided figure
• Hexagon: A six-sided figure
• Heptagon: A seven-sided figure
• Octagon: An eight-sided figure (like octopus)
• Nonagon: A nine-sided figure
• Decagon: A ten-sided figure (like decathlon)

In general, GMAT polygons will be regular polygons, which means that all the sides are the same length and all the angles are equal. Polygons with exactly the same shape and same angle measurements have proportional corresponding side lengths.

No set formula exists for determining the area of a polygon. You need to create quadrilaterals and triangles within the polygon, find their areas, and add them together to get the total area of the polygon. In addition to determining its area, you may have to come up with the sum of a polygon’s interior angles.

### Angle Rule for Polygons

• In any triangle, the sum of the three angles is 180 degrees.
• In any quadrilateral, the sum of the four angles is 360 degrees.

The sum of interior angles of n sided polygon = (n - 2) × 180 degrees

If the polygon is regular, you can also determine the measure of each of the angles. You divide the sum of the angles by the total number of angles.

### Regular Polygons

For a polygon to be regular, it must satisfy both of the following conditions:

1. The polygon must be equilateral: All sides must have the same length
2. The polygon must be equiangular: All angles must have the same measure 