**Introduction:**

In geometry, a polygon is traditionally a plane figure that is bounded by a closed path or circuit, composed of a finite sequence of straight line segments. There are two types of polygon.

- Regular polygon
- Irregular polygon

Regular Polygon is a polygon in which all angles are equal in measure and all sides have the same length.

Polygon with 10 sides and ten angles is called as **decagon**. Decagon has ten sides and ten angles.

Usually, decagon is referred to as regular decagon which means it has equal angles and same length in all sides.

The following figure shows the general structure of polygon 10 sides i.e., decagon.

(Source:
Wikipedia)

**Sum of the interior angles of a polygon 10 sides:**

Divide the polygon with 10 sides i.e., decagon into number of triangles inorder to find the sum of the interior angles of a decagon. We can divide a decagon into eight triangles. We know that sum of the angles in a triangle is 180 degrees. Therefore,

**8 * 180° = 1440°**

So, the sum of the interior angles of a polygon 10 sides is 1440°

**Measure of angle of polygon 10 sides:**

In regular polygon, there are ten equals and ten equal sides. We know that sum of the interior angle is 1440°. So, to find the measure of angle of regular polygon, divide the sum of interior angles by 10, i.e.,

**1440° ÷ 10 = 144°**

So, the measure of the angle of a regular polygon 10 sides(decagon ) is 144°.

**Measure of central angle of polygon 10 sides:**

Inorder to find the measure the central angle of a regular decagon, draw a circle in the middle of a decagon. We know that a circle having 360° around. So,

**360° ± 10 = 36°**

So, the measure of the central angle of regular polygon 10 sides is 36°.

** **

The area of a polygon with 10 sides is given by

Area, A ≈ 7.694208843t^{2}

(or)

Area, A = 2.5dt

Where, t = edge length

d = distance between parallel sides