# Regular Hexagon Formula

Last Updated : 30 Dec, 2023

Hexagons are polygons that have six sides. Regular hexagons, irregular hexagons, and concave hexagons are the three different varieties of hexagons. The hexagon is called a Regular Hexagon if all of its sides are equal and all of its angles are the same. A regular pentagon has five equal sides, whereas a regular octagon has eight equal sides. When such prerequisites are not satisfied, polygons can take on the appearance of a variety of irregular shapes. When six equilateral triangles are placed side by side, a regular hexagon is formed. The area of the regular hexagon is thus six times the size of the identical triangle.

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Properties of Regular HexagonÂ

1. It has six equal sides and six identical angles.
2. It has six vertices.
3. The sum of the inner angles equals 720Â°.
4. The inside angle is 120Â° while the external angle is 60Â°.
5. It consists of six equilateral triangles.
6. Within a regular hexagon, 9 diagonals can be drawn.
7. All of the opposite sides are parallel.

### Regular Hexagon Formulae

There are specific formulae for the area of a regular hexagon and the perimeter of the regular hexagon. Let’s take a look at the regular hexagon formulae,

Area of Regular HexagonÂ

It is defined as the area occupied inside the boundary of a hexagon.

Area of an Hexagon = {(3âˆš3a2 )/2}

Here ‘a’ represents the side of hexagon.

Perimeter of Regular HexagonÂ

The perimeter of a hexagon is defined as the length of the hexagon’s border. As a result, the perimeter will equal the total of the lengths of all sides. The perimeter of a hexagon may be calculated using the following formula,

Perimeter = 6 Ã— side length of hexagon

P = 6sÂ

### Sample QuestionsÂ

Question 1: Calculate the area and perimeter of a regular hexagon whose side is 5 cm.

Solution:Â

Given, side of the hexagon = 5 cm

Area of an Hexagon = {(3âˆš3a2 )/2}

= {[(3âˆš3)52 ]/ 2}

= (3âˆš3 Ã— 25)/2

= 75âˆš3 / 2Â

= (75 Ã— 1.7320)/2

= 64.95 sq.cm

Perimeter of the hexagon = 6s

= 6 Ã— 5Â

= 30 cm

So the area of hexagon is Â 64.95 sq.cm and perimeter of hexagon is 30 cm.

Question 2: Find the area of the board if the perimeter of a hexagonal board is 25 cm?

Solution:Â

Given, perimeter of the board = 25 cm

Perimeter of an Hexagon = 6s

25 = 6s

s = 25/6

= 4.166

Area of an Hexagon = {(3âˆš3a2 )/2}

= {[3âˆš3(4.166)2 ]/2}

= {[(3âˆš3) 17.3555 ]/2}

= (3 Ã— 1.7320 Ã— 17.3555) /2

= 90.179 / 2

= 45.089 cm2.

Question 3: Â A hexagonal board has a perimeter equal to 18 inches. Find its area.

Solution:Â

To Find: Area of the hexagon.

Given: Perimeter of hexagonal board = 18 Â inches.

The perimeter of hexagon = 6s

18 = 6s

s = 18/6

s = 3

Side = 3 inches.

Now Use the hexagon formula for Area,Â

Â Area of an Hexagon = {(3âˆš3a2 )/2}

= {(3âˆš3 Ã— 32 )/2}

= {(3âˆš3 Ã— 9 ) /2}

= {3 Ã— 1.7320 Ã— 9} / 2

= 46.764 / 2

= 23.382 sq. inchesÂ

Question 4: Determine the side length of the regular hexagon whose perimeter is 42 units.

Solution:Â

To Find: Side length of hexagon

Given: Perimeter = 42 units.

Using the hexagon formula for perimeter

Perimeter of Regular hexagon = 6s

42 = 6s

Side = 42/6

Side = 7Â

So, the side length of the regular hexagon whose perimeter is 42 units is 7 unit.

Question 5: Evaluate the length of the side of a regular hexagon if its perimeter is given as 60 cm.

Solution:Â

Given, perimeter = 60 cm

Using the hexagon formula for perimeter

Perimeter of Regular hexagon = 6s

Therefore, 60 = 6s

Or, s = 60/6Â

= 10 cm
So, the length of the side of a regular hexagon whose perimeter 60 cm is 10 cm.

Question 6: Â Find the area and perimeter of the hexagon, if all its sides have a length equal to 7 cm.

Solution: Â

To Find: Area of the hexagon and Perimeter of hexagon.

Given: Side = 7cm

The perimeter of hexagon = 6s

= 6 Ã— 7

= 42 cm

Now Use the hexagon formula for Area,Â

Area of an Hexagon = {(3âˆš3a2 )/2}

= Â {(3âˆš3 Ã— 72 )/2}

= {(3âˆš3 Ã— 49 ) /2}

= {3 Ã— 1.7320 Ã— 49} / 2

= 254.60 / 2

= 127.302 sq. cmÂ

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