## GMAT Quantitative Review

## 3.0 Math Review

### 3.3 Geometry

### 5. Polygons (Convex)

A *polygon* is a closed plane figure formed by three or more line segments, called the *sides* of the polygon. Each side intersects exactly two other sides at their endpoints. The points of intersection of the sides are *vertices*. The term “polygon” will be used to mean a convex polygon, that is, a polygon in which each interior angle has a measure of less than .

The following figures are polygons:

The following figures are not polygons:

A polygon with three sides is a *triangle*; with four sides, a *quadrilateral*; with five sides, a *pentagon*; and with six sides, a *hexagon*.

The sum of the interior angle measures of a triangle is . In general, the sum of the interior angle measures of a polygon with *n* sides is equal to . For example, this sum for a pentagon is .

Note that a pentagon can be partitioned into three triangles and therefore the sum of the angle measures can be found by adding the sum of the angle measures of three triangles.

The *perimeter* of a polygon is the sum of the lengths of its sides.

The commonly used phrase “area of a triangle” (or any other plane figure) is used to mean the area of the region enclosed by that figure.