# GRE Geometry | Polygons

**Polygons:**

The word polygon is derived from the Greek word polugonon, here poly means many and gons means angles. Polygons can be defined as a closed curve made up of line segments. Each line segment will become sides of the polygon.

**Classification of polygons:**

On the basis of the number of sides polygons are classified as follows:

For n sides, we can call it n-gon. From here we can observe that the triangle is a polygon with least number of sides.

**Concave and Convex polygon:**

Convex polygons are the polygons whose all diagonal lie inside the figure and Concave polygons are those whose any diagonal lie outside the figure.

**Regular and Irregular polygon:**

Regular polygons are the polygons having all sides of equal length and Irregular polygons are the polygons having different side length.

**Note:**

- For a polygon, Exterior angle + Interior angle = 360°
- The sum of all exterior angles of polygon is 360°
- In a regular polygon all interior angles are equal.
- In a regular polygon all exterior angles are also equal.
- For a regular polygon, Number of sides = 360/exterior angle.
- Sum of all interior angles of a polygon is given by (n-2)*180, where ‘n’ is the number of sides in the polygon.
- Area of a polygon means area enclosed by the polygon and Perimeter of a polygon is sum of all the side length.

**Examples:**

**Example-1:**What is the sum of all interior angles of heptagon ?**Solution:**Since it is a Heptagon, number of sides (n) = 7 Sum of all interior angles = (n-1)*180

So, for heptagon sum of interior angles = (7-2)*180 = 900

**Example-2:**Calculate the number of side in a regular polygon having exterior angle 45° ?**Solution:**Number of sides = 360/exterior angle Since exterior angle is 45° number of sides = 360/45 = 8

**Example-3:**What will be the value of an interior angle for a regular hexagon?**Solution:**Since it is a hexagon, number of sides (n) = 6 exterior angle = 360°/6 = 60 we know that, interior angle + exterior angle = 180° interior angle + 60° = 180° interior angle = 180° - 60° interior angle = 120 °

**Example-4:**Exterior angle of a regular polygon is 8°.(a) find the number of sides in the polygon? (b) find the interior angle of the polygon?

**Solution:**(a) Number of sides = 360°/8°= 45 (b) interior angle = 180°- 8° = 172