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.
We can calculate the area and perimeter of hexagonal objects using specific formulas related to a hexagon. Among other things, you will find a hexagon in a honeycomb, a quartz crystal, a bolt head, lug or a wheel nut, an Allen wrench or even in the design of floor tiles.
To obtain the area of each form in the instance of an irregular hexagon, divide the hexagon into rectangles and right triangles. To find the perimeter of the shape, just add the lengths of all its sides.
The length of the boundary of a hexagon is its perimeter. The perimeter is equal to the total length of all its sides.
There are nine diagonals in a hexagon.
Each interior angle of a regular hexagon measures 120 degrees.