Before knowing about a hexagon let us know about a polygon.This article is on Area of Hexagon.

### 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.

### 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 “

**” is the height of the hexagon when it is made to lie on one of the bases of it.**

*h***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 ×

*l*

^{2}

Here, side *l* = 7 cm

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

Area = 33√2332 × 7^{2}

= 127. 31 cm^{2} .

**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 cm^{2}.

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