Hexagon Formula

Hexagon Formula

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

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

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

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

4. 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

1. 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. 

2. 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. 

3. 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.