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# Hendecagon

We study about different types of shapes in geometry. Polygons belong to an important family of geometrical shapes. A polygon is defined as a two-dimensional figure that is composed of a number of angles and sides. It is a closed figure made up of at least three straight lines. There are different types of polygons which are triangle (3 sides), quadrilateral (4 sides), pentagon (5 sides), hexagon (6 sides), heptagon or septagon (7 sides), octagon (8 sides) and so on.

Hendecagon is a type of polygons which has 11 sides or 11 vertices. It eventually has 11 angles. It is also called as undecagon. There are a number of properties that uniquely identify a hendecagon. Like other polygons, hendecagons are of two types - regular and irregular. A regular hendecagon has 11 equal sides as well as 11 equal interior angles. On the other hand, an irregular one has unequal sides and angles. A regular hendecagon is illustrated by the following diagram :

The measure of each interior angle of a regular hendecagon is 147$^{\circ}$ as shown above and its exterior angles measure 33$^{\circ}$. Hendecagons, whether regular or irregular, are seen in mathematics too often. It is also found in our surroundings very commonly. In this chapter, we shall learn about a hendecagons in detail.

## Hendecagon Definition

A Hendecagon is a polygon with 11 sides and 11 angles. Regular Hendecagon has 11 equal number of angles. The measure of each internal angle is 147.27$^o$.

Regular hendecagon has: 11 sides equal and 11 angles equal.

## Properties of a Hendecagon

Given below are some of the formulas involved in a regular hendecagon with side length t.

• Area of a hendecagon = 9.36 t2.
• Number of all possible diagonals in a hendecagon = $\frac{n(n-3)}{2}$ = $\frac{88}{2}$ = 44
• Perimeter of a hendecagon = 11 t.
• Exterior angle of a hendecagon = 33º.
• Interior angle of a hendecagon at each vertex = 147º.
• The sum of all the interior angles in an undecagon = (n - 2) 180 degrees = 9 x 180 degrees = 1620º.
• Inradius of an undecagon = 1.70 t.
• Circum radius of an undecagon = 1.77 t.

## Hendecagon Angles

A hendecagon is an 11 sided polygon. Each internal angle of a regular hendecagon = 147.27$^o$.

The sum of interior angles of a hendecagon = (n - 2) * 180o = (11 - 2) · 180o = 1,620o.

The central angle of a regular hendecagon measures = $\frac{360^o}{n}$ = $\frac{360^o}{11}$ = 32.73o.

## Hendecagon Examples

Given below are some examples based on hendecagon.

### Solved Examples

Question 1: The side length of the regular undecagon is 4.2 cm. Find the area of undecagon.
Solution:

Side length of the undecagon (t) = 4.2 cm

The formula for calculating the area of the regular undecagon = 9.36 t2.

= 9.36 (4.2)2

= 9.36 * 17.64 = 165.11 cm2.

Question 2: The inradius of a given undecagon is 7.3 cm. Find the area of the regular undecagon.
Solution:

The inradius of undecagon = 1.70 t.

7.3 = 1.70 t

t = $\frac{7.3}{1.70}$ = 4.28 cm

The formula for area of an regular undecagon = 9.36 t2.

= 9.36 (4.28)2.

= 9.36 x 18.32 = 171.46 cm2.