Polygon

Let Us Learn About Polygon

A polygon is a closed figure that is the union of line segments in a plane. A polygon has three or more sides. A polygon has the same number of angles as sides.

Polygons can be classified as either convex or concave.

A polygon is convex if no line that contains a side of the polygon contains a point in the interior of the polygon. In a convex polygon, each interior angle measures less than 180 degrees.

Concave polygons "cave-in" to their interiors, creating at least one interior angle greater than 180 degrees (a reflex angle).

Unless otherwise stated, we will be discussing convex polygons.

Listed below are some of the more commonly used polygons.

Types Of Polygon

A polygon is equilateral if all of its sides are of the same length.
A polygon is equiangular if all of its angles are of equal measure.

A regular polygon is a polygon that is both equilateral and equiangular.

Sum of Interior Angles of a Polygon = 180(n-2)

Each interior angle of a "regular" polygon = 180(n-2)/n

Sum exterior angles of any polygon = 360° (using one exterior angle at a vertex)

Each exterior angle (regular polygon) = 360/n

Standard Polygons:

The different standard polygons are:

1. Square

2. Rectangle

3. Parallelogram

4. Triangle

5. Rhombus

6. Trapezium / Trapezoid

Regular Polygon

Definition of Regular Polygon

• A polygon having all its sides equal and all the angles equal is called a Regular Polygon.

More about Regular Polygon

• The measure of each angle of a regular polygon with n sides is given as(n-2) x 180/n degrees.
• A circumscribed circle can be drawn through all the vertices of a regular polygon.