### Area of Pentagon | Properties | Definition | Perimeter | Formula

A pentagon is a type of polygon which have 5 sides and 5 angles. Here you will learn the Area of Pentagon | Properties | Definition | Perimeter | Formula.

## What is Pentagon?

A pentagon is a polygon with 5 sides. It could be a convex pentagon or a concave pentagon, which is a self-intersecting 5 sided closed figure

### Type of Pentagon

• Regular and Irregular pentagon
• Convex and Concave pentagon

### Regular and Irregular pentagon

If all the sides are equal in length, and five angles are of equal measure is called Regular. If the pentagon does not have equal side length and angle measure, then it is known as an irregular pentagon.

The apothem of a regular polygon is the line from the center to the midpoint of a side. (or, the length of that line). It is also the radius of the incircle.

### Convex and Concave pentagon

If all the vertices of a pentagon are pointing outwards, it is known as a convex pentagon. If a pentagon has at least one vertex pointing inside, then the pentagon is known as a concave pentagon.

### Area of Pentagon

For regular pentagon

Area = (5/2) × Side Length ×Apothem square units

If only the side length of a pentagon is given, then

Area = 5s2 / 4 tan 36° Square units

If only the radius of a pentagon is given, then

Area =(5/2)r2 sin 72° Square units

### Perimeter of Pentagon

The perimeter of a square found by adding all the sides.

Perimeter = s + s + s + s + s
Perimeter = 5s

P = 2 x side units

### Properties of Pentagon

• Sum of the interior angles is equal to 540°
• An equilateral pentagon has 5 equal side
• The measure of the interior angle of a regular pentagon is 108 degree
• The measure of the central angle of a regular pentagon is 72 degrees.