Hexagon Formula
Hexagon Formula
A polygon that will have 6 sides is known as a hexagon. There are several types of hexagons. Regular hexagons, irregular hexagons, and concave hexagons are some types of hexagons. If all the sides of a hexagon are equal and the angles are equal, the hexagon is said to be a regular hexagon. A hexagon has a total of nine diagonals. The sum of the interior angles of a regular hexagon is always 720 degrees and each interior angle is 120 degrees. The exterior angles of a regular hexagon are 60 degrees, and the sum of all exterior angles is 360 degrees. Use the Hexagon Formula to calculate its area and perimeter. Students can find study materials associated with the topic on the Extramarks learning portal.
What Is Hexagon Formula?
A Hexagon Formula is defined as a set of formulas that calculate the perimeter, area, and diagonal of a hexagon. The Hexagon Formula applies directly to regular hexagons.
Hexagon Formula
A polygon is always a two-dimensional (2-D) closed figure made up of straight line segments. In Geometry, a hexagon will always be a six-sided polygon. If all sides have the same length and all angles have the same size, such a hexagon is called a regular hexagon. That is, the sides of a regular hexagon are congruent.
There is a set of predefined formulas for calculating the perimeter and area of regular hexagons, collectively called the Hexagon Formula. The formula for a hexagon with side length a is:
- Properties of a regular hexagon:
It has 6 sides and 6 corners and all sides have the same length and all angles have the same size also the total number of diagonals in a regular hexagon is 9. The sum of all interior angles is 720 degrees and each interior angle is 120 degrees. The sum of all exterior angles is 360 degrees and each exterior angle is 60 degrees. Imagine a regular hexagon with units on each side.
- Hexagon Area Formula: The hexagon area is defined as the area occupied within the boundaries of the hexagon.
To calculate the area of a hexagon, divide it into 6 smaller isosceles triangles. After calculating the area of one of the triangles, one can multiply by 6 to get the total area of the polygon.
Derivation Of Hexagon Formula
The Hexagon Formula can be written as:
Area of hexagon:
(3√3s.s)/2
Where,
s = side length. The perimeter of the hexagon: 6s
Where,
s = side length. Hexagon diagonals: 2s and √3s
Where,
s = side length
Special formula: Area = 1/2 x Perimeter x Apothem
Students can see the application of the hexagonal formula in the following solved example. Derivation of the Hexagon Formula Considering a regular hexagon with side a, the area of the hexagon would be as follows.
Divide the hexagon into 6 smaller isosceles triangles. Calculate the area of one of the triangles. Multiply by 6.
(3√3s.s)/2
- Perimeter of hexagon
The perimeter of a polygon is the sum of the lengths of all its sides and a regular hexagon has six sides. So multiply the side length by 6. So the formula for the perimeter of a regular hexagon is: P=6×a
- Hexagonal diagonal
A hexagon has 6(6-3)/2 = 9 diagonals
These 9 diagonals form 6 equilateral triangles. d = 2s for long diagonals and d = √3s for short diagonals where s refers to the side of the hexagon. So the formula for the diagonal of a hexagon is: d = 2s and √3s
Solved Examples Using Hexagon Formula
- Example 1: Compute the perimeter and area of a regular hexagon with sides of 4 units.
To find: Perimeter and area of a hexagon
Given: s= 4 units. Use Hexagon Formula for perimeter
Circumference (P) = 6s
P =6×Four
P = 24 units
Use the regular Hexagon Formula for the area
area of hexagon
=
(3√3s.s)/2
= 41.56 units2
Answer: The perimeter and area of a hexagon are 24 units and 41.56 units2
- Example 2: A hexagonal board has a circumference of 12 inches. find its area.
The objective of the question is to find the area of a hexagon. Given: Circumference = 12 inches. The perimeter of the hexagon = 6s
12 = 6 seconds
s = 2 inches. Using the Hexagon Formula for the area, the area of the hexagon
= (3√3s.s)/2
= 10.39 square inches
Answer: The area of the hexagonal plate is 10.39 square inches.
- Example 3: Find the side length of a regular hexagon with a perimeter of 24 units.hexagon side length
Given: perimeter = 24 units. Use Hexagon Formula for perimeter (P) = 6s
24 =6×s
s = 24/6 units
= 4 units
Answer: A hexagon has a side length of 4 units.
FAQs (Frequently Asked Questions)
1. What is the Hexagon Formula in geometry?
The Hexagon Formula calculates the perimeter, area, and diagonal of a hexagon. The hexagon formula applies directly to regular hexagons. The formula for a hexagon is given by: area of hexagon = (3√3s.s)/2
Hexagon perimeter = 6s, where s = side length.
2. What is the s in the Hexagon Formula?
In the Hexagon Formula, the area of the hexagon is = (3√3s.s)/2
The perimeter of the hexagon = 6s, and s refers to the side of a regular hexagon.
3. How do you use the Hexagon Formula?
To use the Hexagon Formula for a specific hexagon
- Step 1: Identify whether a given hexagon is regular or irregular.
- Step 2: Identify the sides of the regular hexagon.
- Step 3: Substitute the values into the appropriate expressions. Area of hexagon =(3√3s.s)/2
The perimeter of the hexagon would be = 6s
4. What is the Hexagon Formula for irregular hexagons?
For irregular hexagons, find the area of each shape by dividing the given hexagon into rectangles and right triangles and calculating the perimeter by simply adding the lengths of all sides.
