### Polygon

The most basic explanation is that a polygon is a shape made up of at least 3 line segments. These line segments are called edges and the intersecting points are the vertices.
There are two types of polygons: convex and concave.
Convex: Every interior angle of the polygon is less than 180º.
Concave: There is at least one interior angle which is greater than 180º.

Now we will see the Nomenclature of some polygons with various number of edges.

 Name number of edges triangle (or trigon) 3 quadrilateral (or tetragon) 4 pentagon 5 hexagon 6 heptagon (or septagon) 7 octagon 8 nonagon (or enneagon) 9 decagon 10

### Hexagon

Now we can understand that a hexagon is a six-sided polygon. Now, we can appreciate the subtle difference between a regular and irregular hexagon.
Regular hexagon: All the 6 edges and 6 angles are equal. The regular hexagon consists of six symmetrical lines and rotational symmetry of order of 6.
Irregular Hexagon: At least one edge and angle is not equal.

Regular Hexagon                                                            Irregular Hexagon

### Area Of Hexagon

There are various ways to calculate the area of Hexagon. The various methods are mainly based on how you divide the hexagon. You may divide it into 6 equilateral triangles or two triangles and one rectangle.

Method 1:

So we will use the most popular and easy way to get the area in which we divide the hexagon into 6 equilateral triangles of side l.

So, Area (equilateral triangle) = (√3/4)*l*l

So, Area (hexagon) = 6*(√3/4)*l*l = 3*(√3/2)*l*l

Method 2:

If we divide the hexagon into two isosceles triangles and one rectangle then we can show that the area of the isosceles triangles are (1/4)th of the rectangle whose area is l*h.

So, we get another formula that could be used to calculate the area of regular Hexagon:

Area= (3/2)*h*l

Where l is the length of each side of the hexagon and “h” is the height of the hexagon when it is made to lie on one of the bases of it.

NOTE:
The apothem height of a hexagon is half of the total height of a hexagon.

### Examples:

Question 1: Find the area of hexagon(regular) whose side is 7 cm.
Solution:   Step 1: Area of a hexagon equation is A = (3√3)/2 × l2

Here, side l = 7 cm

Step 2: Substitute the value of side in area formula,

Area = 332332 × 72

= 127. 31 cm2 .

Question 2: If the base length is 4 cm and apothem height is 16 cm, then find the area of the hexagon.
Solution:   Step 1: Area of a hexagon = (3/2) × b × h

Step 2: Here apothem height is given so we need to multiply it by 2 and substituting the value in the above formula, we get

= (3/2) × 4 × (16*2)

= 192 cm2.

Also check out our article on Area of an equilateral triangle here.

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