## Hexagon Formula

A hexagon is a type of polygon which has six sides. There are four main types of a hexagon they are:

Regular hexagon – If all the sides and angles are equal then it is a regular hexagon.

Irregular hexagon – If all the sides and angles are not equal then it is an irregular hexagon.

concave hexagon – Concave hexagon has at least one interior angle greater than 180 degree.

Convex hexagon – Convex hexagon has no interior angle greater than 180 degree.

A hexagon has 9 total diagonals and the total of all interior angles of a regular hexagon is 720 degrees in which each interior angle is 120 degrees and the total of all exterior angles of a regular hexagon is 360 degrees in which each exterior angle is 60 degrees.

Hexagon Formula consist set of formulas to calculate the area, perimeter and diagonals of a hexagon.

Area of hexagon = 3√3s²/2

The perimeter of the hexagon = 6s

Where s = side length

## Derivation of Hexagon Formula

### Area of Hexagon

Firstly divide the hexagon into small six isosceles triangles then find the area of any one of that triangles and then multiply it by 6 thus we get,

3⇃3s²̍̍̍

= 𝄖𝄖𝄖𝄖

2

**Perimeter of Hexagon**

The perimeter of a hexagon can be found by multiplying the side lengths by 6 as a hexagon has 6 sides.

Thus, the formula for the perimeter of a hexagon is given as P=6*a.

**Diagonal of Hexagon**

The hexagon has 9 diagonals and this diagonal forms six equilateral triangles.

So for longer diagonal d = 2s and for shorter diagonal d = ⇃3s where s represents the side of the hexagon.

Thus, the formula for diagonal is given as d=2s and d=⇃3s.

## Examples

Calculate the perimeter and the area of a regular hexagon having sides equal to 5 units.

The perimeter of hexagon = 6s

Therefore, P = 6*5

P = 30 units

Area of hexagon = 3⇃3s²̍̍̍

𝄖𝄖𝄖𝄖

2

3⇃3 * 5²̍̍̍

= 𝄖𝄖𝄖𝄖

2

= 64.875 units²

Thus the perimeter and area of a hexagon are 30units and 64.875units².

A hexagonal board has a perimeter equal to 24 inches. Find its area.

P = 6s

24 = 6s

s = 4 inches

Area of hexagon = 3⇃3s²̍̍̍

𝄖𝄖𝄖𝄖

2

3⇃3 * 4²̍̍̍

= 𝄖𝄖𝄖𝄖

2

= 41.52 inches²

Thus, the area of the hexagonal board is 41.52 inches².

Determine the side length of a regular hexagon whose perimeter is 36 units.

P = 6s

36 = 6s

s = 24/6

s = 6 units

Thus the side length of the hexagon is 4 units.