The two-dimensional shapes with number of sides at least three are called as polygons. The polygons with 13 sides are called as Tridecagon or other wise called as triskaidecagon. The regular decagon has 12 equal sides and angles. The Tridecagon cannot be constructed with compass and ruler. In this article we will see about the polygon with the 13 sides in detail.

## More about the Polygon with 13 Sides:

A regular polygon with 13 sides will be having 13 equal sides with all its internal angle measurements the same. The Tridecagon has 13 vertices and the **external angles** are also equal. In a irregular Tridecagon unequal sides and angles.

The sum of internal angles in Tridecagon is = (13 – 2) * 180 degrees = 1980°

The internal angle at a single vertex is = 152.308°.

The total external angle of a Tridecagon = 360°.

The formula for calculating the area of the Tridecagon of side length S,

** Area = 13.18 S ^{2}**

The perimeter of the Tridecagon is = 13 * S.

The area using the inradius of the Tridecagon is,

** Area = 3.204 r ^{2}.**

The area formula using the circumradius is,

** Area = 3.02 R ^{2}**

## Example Problems on Polygon with 13 Sides:

**Example 1:**

Find the area of the Tridecagon with a side length of 5cm.

**Solution:**

Area of the Tridecagon = 13.18 S^{2}

= 13.18*(5)^{2}

= 13.18*25

= 329.5 cm^{2}

**Example 2:**

Find the area of the Tridecagon with an inradius of 4.5cm.

**Solution:**

Area of the Tridecagon = 3.204 r^{2}

= 3.204*(4.5)^{2}

= 3.204*20.25

= 64.9 cm^{2}

**Example 3:**

Find the area of the Tridecagon with a circumradius of 6cm.

**Solution:**

Area of the Tridecagon = 3.02 R^{2}

= 3.02*(6)^{2}

= 3.02*36

= 108.7 cm^{2}

## Practice problems on polygon with 13 sides:

**Problem 1:**

Find the area of the Tridecagon with a side length of 5.5cm.

**Answer: 398.7 cm ^{2}.**

**Problem 2:**

Find the area of the Tridecagon with a circumradius of 6.2cm.

** Answer: 116.1 cm ^{2}.**

**Problem 3:**

Find the area of the Tridecagon with an inradius of 4cm.

** Answer: 51.26 cm ^{2}.**