A polygon having six sides and six angles is called a Hexagon. Regular hexagons have six equal sides and six angles and are composed of six equilateral triangles. There are a variety of ways to calculate the area of a hexagon, whether you're working with an irregular hexagon or a regular hexagon.There are various ways to determine the area of hexagon formula . The various methods are mainly based on how you spit the hexagon. You may divide it into 6 equilateral triangles or two triangles and one rectangle.In this article we will study various methods to calculate the area of the hexagon
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Where s is the sides of the hexagon
Types of hexagona can be classified as follows:
Regular Hexagon
Irregular Hexagon
In the case of a regular hexagon, all the sides are of equal length and the internal angles are of the same value.Whereas in the case of irregular hexagons, neither the sides are equal, nor the angles are the same.
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Regular Hexagon Irregular Hexagon
There are several ways to find the area of a hexagon.
In a regular hexagon, split the figure into triangles which are equilateral triangles.
Find the area of one triangle.
Multiply this value by six.
Alternatively, the area can be found by calculating one-half of the side length times the apothem.
The area of Hexagon formula is given by
Area of Hexagon = 3√3/2 x s2
where “s” denotes the sides of the hexagon.
Second area of regular hexagon formula is given by:
Area of Hexagon = 3/2 x s x h
Where “s” is the length of each side and “h” is the height of the hexagon when it is made to lie on one of the bases of it.
Method 1
One of the easiest methods that can be used to find the area of a polygon is to split the figure into triangles. Let's start by splitting the hexagon into six triangles.
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In this figure, the center point,x, is equidistant from all of the vertices. As a result, the six dotted lines you can say diagonals within the hexagon are of the same length. Likewise, all of the triangles within the hexagon are congruent by the side-side-side rule: each of the triangle's share two sides inside the hexagon as well as a base side that makes up the perimeter of the hexagon. In a similar fashion, each of the triangles have the same angles. There are
3600 in a circle and the hexagon in our image has separated it into six equal parts; therefore, we can write the following:
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θ=3600/6
θ=600
We also know the following:
∠AXB=∠BXC=∠CXD=∠DXE=∠EXF=∠FXA=600
Now, let's look at each of the triangles in the hexagon. We know that each triangle has two two sides that are equal; therefore, each of the base angles of each triangle must be the same. We know that a triangle has 180 and we can solve for the two base angles of each triangle using this information.
2x + 600 = 1800
2x = 1200
x = 600
Each angle in the triangle equals 600
We now know that all the triangles are congruent and equilateral: each triangle has three equal side lengths and three equal angles. Now, we can use this vital information to solve for the hexagon's area. If we find the area of one of the triangles, then we can multiply it by six in order to calculate the area of the entire figure.
We have, Area of equilateral triangle = (√3/4) x s x s
So, Area of hexagon = 6 x (√3/4) x s x s
+= 3 x (√3/2) x s x s
Area of Hexagon = 3 √3/2 x s2
Method 2
If we divide the hexagon into two isosceles triangles and one rectangle then we can show that the area of the isosceles triangles are (1/4)th of the rectangle whose area is l*h.
So, area of regular Hexagon formula is given by:
Area= (3/2) x h x s
Where “s” is the length of each side and “h” is the height of the hexagon when it is made to lie on one of the bases of it.
Solved Examples
Example 1: Find the area of a regular hexagon whose side is 7 cm.
Solution:
Formula of regular hexagon is = 3√3/ 2 x s2
where, s = side = 7 cm
Substitute the value of side in area formula,
Area = (3 x 1.7320) / 2 x 7 x 7
= 127. 31 cm2.
Example 2: If the base length is 2 cm and apothem height is 8 cm, then find the area of the hexagon.
Solution: Formula of regular hexagon = (3/2) × s × h
Here apothem height is given so we need to multiply it by 2 and substituting the value in the above formula, we get
= (3/2) × 2 × (8*2)
= 48cm2.
1. What is Polygon?
Answer: A polygon is a simple closed curve. A two-dimensional closed figure bounded with three or more than three straight lines is called a polygon. Triangles, square, rectangle, pentagon, hexagon, are some examples of polygons.
The segments are referred to as the sides of the polygon. The points at which the segments meet are called vertices. Segments that share a vertex are called adjacent sides. A segment whose endpoints are nonadjacent vertices is called a diagonal. See the picture below.
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The below figures show some of the examples of polygons or polygonal curves( a closed curve that is not a polygon).
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In figure 1 you can see that all the shapes are polygons, as all the shapes are drawn joining the straight lines only. There are no curved lines..
But in figure 2 the shape is not a polygon because it is not fully connected and also has curved lines and such shapes that have curves are called a closed curve that is not a polygon.
2. State some of the popular polygons along with its number of sides and Measure of Interior Angles.
Answer: Here is the list of some of the regular polygons with the number of polygon sides, shapes, and measures of its interior angles.
Name | Number of Polygon Sides | Shape | Measures of Interior Angles |
Triangle | 3 | [Image will be uploaded soon] | 60^{0} |
Quadrilateral | 4 | [Image will be uploaded soon] | 90^{0} |
Pentagon | 5 | [Image will be uploaded soon] | 108^{0} |
Hexagon | 6 | [Image will be uploaded soon] | 120^{0} |
Heptagon | 7 | [Image will be uploaded soon] | 128.571^{0} |
Octagon | 8 | [Image will be uploaded soon] | 135^{0} |
Nonagon | 9 | [Image will be uploaded soon] | 140^{0} |
Decagon | 10 | [Image will be uploaded soon] | 144^{0} |
Hendecagon | 11 | [Image will be uploaded soon] | 147.273^{0} |
Dodecagon | 12 | [Image will be uploaded soon] | 150^{0} |
Triskaidecagon | 13 | - | 152.308^{0} |
Tetrakaidecagon | 14 | - | 154.286^{0} |
Pentadecagon | 15 | - | 156^{0} |
n-gon | n | [Image will be uploaded soon] | (n−2) x 180° / n |