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Hexagon Formula

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A hexagon is a closed polygon that consists of six-line segments and six internal angles. A regular hexagon is one in which the lengths of all the sides and the measurements of all the angles are equal.

Hexagon Definition

A hexagon is termed as a polygon with six sides. Hexagons are classified into three types: regular hexagons, irregular hexagons, and concave hexagons. A hexagon is called a regular hexagon if all of its sides are equal and all of its angles are the same.

Hexagon Formula

A specified set of formulae for calculating the perimeter and area of a regular hexagon is known as the hexagon formula.

Hexagon Formula

Hexagon 

The hexagon formula for a hexagon with side length s is as follows :

Area of Hexagon

The formula for Area of Hexagon is 

Area = (3√3s2) / 2 

here s is the side of hexagon

Perimeter of Hexagon

The formula of Perimeter of Hexagon is 

Perimeter = 6s 

here s is the side of Hexagon

Hexagon Properties

  • It is made up of six sides and six angles.
  • All of the sides’ lengths and angles’ measurements are equal.
  • A regular hexagon has a total of nine diagonals.
  • The sum of all internal angles is 720 degrees, with each inside angle measuring 120 degrees.
  • The sum of all external angles is 360 degrees, with each exterior angle measuring 60 degrees.

Solved Problems on Hexagon

Problem 1: Calculate the perimeter and area of a regular hexagon having a side equal to 5 units.

Solution: 

To Find : Perimeter and Area 

Given : s = 5 units.

Using the hexagon formula for perimeter

Perimeter(P) = 6s

P =  6 × 5

P = 30 units

Using the regular hexagon formula for Area

                       = (3√3s2 ) / 2 

                       = {(3√3(5)2 }/ 2 

                       =  {(3√3 (25)} / 2 

                       = (3 x 1.7320 x 25 ) / 2

                       = 129.9/ 2

                       =  64.95 sq. unit 

Therefore the perimeter of Hexagon is 30 units and area is 64.95 sq. units .

Problem 2: A hexagonal board which has a perimeter of 18 inches. Find its area.

Solution: 

To Find : Area of the hexagon.

Given : Perimeter = 18 inches.

The perimeter of hexagon = 6s

18 = 6 s 

s = 18/6

   =  3 inches.

Using the hexagon formula for Area :

Area of hexagon

= { 3√3(3)2 } / 2 

= { 3 x 1.7320 x 9 } / 2

= 46.764 / 2

=  23.382 sq. inches .

therefore the Area of hexagonal board is 23.382 sq . inches .

Problem 3: Determine the side of the regular hexagon whose perimeter is 30 units.

Solution: 

To Find : Side of hexagon = s

Given : perimeter = 30 units.

Using the hexagon formula for perimeter

Perimeter(P) of hexagon  = 6s

30 = 6 × s

  s = 30/6 units

    = 5 units

hence the side of hexagon is 5 units .
 

Problem 4: What is the area of a regular hexagon whose side length is equal to 6 cm?

Solution: 

As we know ;

Area of hexagon = (3√3 s2)/2

                   Area = {3√3 (6)2 /2

                   Area = { 3 × 1.7320 × 36 } / 2

                           =  187.056/ 2

                           =  93.52 sq . cm

hence the area of hexagon is 93.52 sq . cm 

Problem 5: Determine the side of the regular hexagon whose perimeter is 72 units.

Solution: 

To Find : Side of hexagon = s

Given : perimeter = 72 units.

Using the hexagon formula for perimeter

Perimeter(P) of hexagon  = 6s

72 = 6 × s

  s = 72/6 units

    = 12 units

Hence, the side of hexagon is 12 units.

FAQs on Hexagon Formula

What Is Hexagon Formula in Geometry?

When referring to a hexagon, especially a regular hexagon (where all sides and angles are equal), these key formulas are commonly used:

  1. Perimeter of a Hexagon: The perimeter P of a regular hexagon (where all sides are of equal length a) is given by: P = 6a
  1. Area of a Regular Hexagon: The area A of a regular hexagon can be calculated using the formula: A = (3√3)​​a2 where a is the length of one side.

What Is s in Hexagon Formula?

The s in Hexagon Formula refers to the side of the regular hexagon. 

What Is Hexagon Formula For Irregular Hexagon?

For an irregular hexagon, there isn’t a single formula like there is for regular hexagons, because the sides and angles can vary. To find the area of an irregular hexagon, you typically divide it into simpler shapes. Calculating the perimeter is straightforward: sum the lengths of all six sides.


Last Updated : 12 Feb, 2024
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