Hexagon Formulas | List of Hexagon Formulas You Should Know - BYJUS

# Hexagon Formulas

A hexagon is a closed polygon made up of six line segments. It has six edges, six interior angles and six vertices. The perimeter, area or diagonal length of a regular hexagon is calculated using the formulas that are all related to a hexagon....Read MoreRead Less

### What is a Hexagon?

A polygon is a closed, two-dimensional(2-D) geometric shape formed from segments of straight lines. A hexagon is a six-sided polygon in geometry. A hexagon is said to be a regular hexagon if the lengths of all the sides and the measure of all the angles are the same. To put it another way, the sides and angles of a regular hexagon are congruent.

### Properties of a Regular Hexagon

• There are six angles, six vertices and six sides
• Each side length and each angle measurement is the same
• It has nine diagonals in total
• Each interior angle is 120 degrees, hence the sum total of the interior angles is 720 degrees
• Each exterior angle is 60 degrees

### Formulas Related to a Hexagon

There is a collection of formulas used to determine the area, the perimeter, and the diagonals of a hexagon. The measurements in regular hexagons are calculated by applying these formulas for a hexagon.

Let’s take a regular hexagon with side ‘a’ units.  Hence,

Area of a hexagon, A = $$\frac{3\sqrt{ 3 }}{2}$$ x a$$^2$$

Perimeter of a hexagon, P = 6 × a

Diagonal of a hexagon, d = 2a              (for the long diagonal) and,

d = $$\sqrt{ 3 }$$a                                                 (for the short diagonal)

### Solved Examples

Example 1: Determine the area and perimeter of a regular hexagon, if the side length is 37 centimeters.

Solution:

Side length of a hexagon = 37 cm

Area of an Hexagon A = $$\frac{3\sqrt{ 3 }}{2}$$ x a$$^2$$

= $$\frac{3\sqrt{ 3 }}{2}$$ x (37)$$^2$$

= 3556.76 cm$$^2$$

Perimeter of the hexagon P = 6a

= 6 × 37

= 222 cm

So, the area of a hexagon is 3556.76 square centimeters and the perimeter is 222 centimeters.

Example 2: The perimeter of a hexagonal steel sheet is 30 feet. Find the area of the sheet.

Solution

Perimeter of the hexagonal steel sheet P = 30 feet

30  = 6a

5 = a

So the length of one the sides of the hexagon is 5 feet

Area of a hexagon, A = $$\frac{3\sqrt{ 3 }}{2}$$ x a$$^2$$

= $$\frac{3\sqrt{ 3 }}{2}$$ x (5)$$^2$$

= 64.95 ft$$^2$$

So, the area of a hexagon is 64.95 square feet.

Example 3: Find the side length of a regular hexagon, if its perimeter is 11 yards.

Solution:

Perimeter of a hexagon, P = 11 yards

P = 6a

11 = 6a

$$\frac{11}{6}$$ = a

1.833 = a

The side length of the hexagon is 1.83 yards.