Hexagon Formula
Hexagon Formula
A polygon is a two-dimensional, closed shape with multiple sides, each of which is a straight line segment. Among the various types of polygons, a hexagon is a specific kind with six sides. In geometry, if a hexagon is regular, all its sides are of equal length, and all its angles are equal. In other words, the sides of a regular hexagon are congruent. This article will explore the characteristics of a hexagon and present the formulas used to calculate its measurements.
What is a Hexagon?
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.
What Is Hexagon Formula?
The hexagon formula consists of a set of equations used to calculate the perimeter, area, and diagonals of a hexagon. These formulas specifically apply to regular hexagons, where all sides and angles are equal.
Area of Hexagon
A=(3√3)×a2/2
Where, a = side length.
Perimeter of a Hexagon
P = 6 x a
Interior Angle of Hexagon
Each interior angle of a regular hexagon = 720°/6 =120°
Exterior Angle of Hexagon
Each exterior angle of a regular hexagon= 360°/6=60°
Diagonal Formula of Hexagon
- Short diagonal : d1 = √3×a
- Long Diagonal: d2 = 2×a
Special Hexagon Formula
Area = 1/2×perimeter×apothem
Derivation Of Hexagon Formula
Area of Hexagon
To calculate the area of a hexagon, we can divide it into six smaller isosceles triangles. By determining the area of one of these triangles and then multiplying that area by six, we can obtain the total area of the hexagon.
A=(3√3)×a2/2
Where, a = side length.
Permiter of a Hexagon
The perimeter of a hexagon is the sum of the lengths of all its six sides. The formula to calculate the perimeter of a hexagon is given by:
P = 6xa
Sides of a Hexagon
As mentioned earlier, a hexagon, whether regular or irregular, has six sides. These sides are straight and form a closed 2-D shape. The perimeter of a hexagon is found by adding the lengths of all its sides. For a regular hexagon, if the perimeter is known, each side’s length can be calculated by dividing the perimeter by 6:
Length of each side of a regular hexagon= Perimeter/6
However, this method doesn’t apply to an irregular hexagon. In an irregular hexagon, since two or more sides are unequal, the lengths of its sides cannot be determined solely from its perimeter.
Angles of Hexagon
A hexagon has 6 interior angles and 6 exterior angles. The sum of the interior angles of a hexagon is 720. For a regular hexagon, where all interior angles are equal, each interior angle measures:
Each interior angle of a regular hexagon = 720°/6 =120°
The sum of the exterior angles of a hexagon is 360°. For a regular hexagon, where all exterior angles are equal, each exterior angle measures:
Each exterior angle of a regular hexagon= 360°/6=60°
Diagonal of Hexagon
There is no standard formula to determine the diagonals of irregular hexagons. However, in regular hexagons, which consist of six equilateral triangles, there are nine diagonals. Calculating the length of each diagonal is straightforward if the length of one side of the hexagon is known. A regular hexagon has diagonals of two different lengths, making it easier to compute all the diagonals once a side length is given.
Short diagonal : d1 = √3×a
Long Diagonal: d2 = 2×a
Solved Examples Using Hexagon Formula
Example 1: Compute the perimeter and area of a regular hexagon with sides of 4 units.
Solution:
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.
Solution:
The objective of the question is to find the area of a hexagon. Given: Circumference = 12 inches. The perimeter of the hexagon = 6s
12 = 6s
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.
Solution:
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 hexagonal formula 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.
