what is the area of a regular hexagon with a distance from its center to a vertex of 1 cm
The area of hexagon is the region occupied by it, within its half dozen sides. A hexagon is a closed polygon made up of 6 line segments and 6 internal angles. The word hexagon is derived from the Greek words, 'Hexa' which hateful 6 and 'Gonia' ways corners. For a hexagon, the sum of internal bending e'er adds up to 720°. In this article, nosotros volition learn to observe the area of the hexagon using these properties.
What is Surface area of the Hexagon?
Area of a hexagon is the area enclosed inside its half-dozen sides. It is measured in foursquare units such as mii, cm2, yard2,in2, etc. A hexagon is a 2-dimensional closed shape that has six sides and six angles. All the sides are continued to each other through their stop-points every bit shown in figure.
According to the length of sides, the hexagon tin can be of ii types,
(i) Regular Hexagon: A regular hexagon is one whose all 6 sides are equal in length. Besides, the internal angle is equal to
\(\begin{array}{fifty}120^{\circ}\end{array} \)
. The regular hexagon consists of six symmetrical lines and rotational symmetry of order of 6.(ii) Irregular Hexagon: An irregular hexagon is i whose all the sides are of unequal length and angles are of diff measures.
In this article, we are going to learn the area of a regular hexagon, formula, its derivation and examples based on it.
Surface area of Hexagon Formula
The formula for surface area of hexagon is given by:
Area of hexagon = (3√3 southward2)/2
where 's' is the length of side of regular hexagon.
Let us see how to derive this formula.
Derivation of Area of Hexagon
The expanse of the Hexagon has been derived equally follows.
Pace 1: In the first pace, we consider a regular Hexagon with a side length of 's'.
Pace 2: In the second step, we divide the regular hexagon into six equal parts past connecting the opposite vertices with the other vertices. When you lot discover it, you can run into that the hexagon is divided into half-dozen triangles.
Stride 3: We know that the area of a right-angled triangle is:
Area = i/2 (Base of operations) (Height)
Area = 1/two (s.h)
Where "south" and "h" stand up for the base of operations and the height of the triangle, respectively.
Pace 4: The Expanse of each of the triangle has been computed in the step (iii). As there are half-dozen like triangles, therefore the total area of the desired hexagon has been computed as:
Area of Hexagon = 6 x 1/2 (s.h) = 3.due south.h
Where
\(\begin{assortment}{l}h^{2} = southward^{2} – \left ( \frac{due south}{2} \correct )^{ii}\end{array} \)
(Past Pythagoras theorem)\(\brainstorm{array}{l}h = \frac{\sqrt{three}}{two}s\end{array} \)
Therefore, Surface area of Hexagon =
\(\begin{array}{l}A = \frac{3\sqrt{3}}{ii}s^{2}\end{assortment} \)
Thus, the formula for the area of the hexagon is obtained.
Similarly, for other polygons such as octagon, pentagon etc. nosotros can besides compute the expanse.
How to Find Area of Hexagon?
Using the formula derived in a higher place, we can find the expanse of the hexagon.
Area of hexagon = (3√iii s2)/2
- Stride 1: Observe the length of the side of regular hexagon
- Pace 2: Evaluate the area using the formula of surface area of the hexagon (three√3 due southtwo)/ii, where 's' is the side length of hexagon.
Area of Hexagon Using Apothem
Apothem is the straight line drawn from the center and is perpendicular to the side of the hexagon. Thus, using the apothem, the expanse of hexagon is given by:
A = one/two × Apothem × Perimeter of hexagon
Since the perimeter of hexagon is equal to sum of all its sides. If the hexagon is regular and its sides is equal to s, then the perimeter is given by:
Perimeter of hexagon = 6s
Hence,
Expanse of hexagon = 1/ii × a × 6s = 3as
where 'a' is the apothem of the regular hexagon and 'southward' is the length of the side of a regular hexagon.
Related Articles
- Regular Hexagon
- Area Of Hexagon Formula
- Properties of Hexagon
Solved Examples on Area of Hexagon
Q.one: What is the area of a regular hexagon whose side length is equal to 5 cm?
Solution: By the formula, we know;
Area of hexagon = (3√3 sii)/2
A = (3√iii (5)2)/2
A = 65 sq.cm
Q.2: If the apothem of a regular hexagon is 4 cm and the side length is 3 cm, and so find the area of hexagon.
Solution: Given, apothem of hexagon is a = 4 cm
Side length is s = 3 cm
Past the formula, we know;
Expanse of hexagon = 3as
Area = 3 10 four ten 3 = 36 sq.cm.
Frequently Asked Questions on Area of Hexagon
What is the area of hexagon?
Area of hexagon is the total region enclosed within the sides. It is measured in foursquare units such as cm2, m2, inii, etc.
What is the formula for expanse of hexagon?
The expanse of hexagon formula is (iii√3 southwardtwo)/2, where due south is the side of regular hexagon.
What is the formula of area of hexagon using apothem?
The area of hexagon when nosotros know the apothem and length of side of regular hexagon, is given by:
Expanse = iii x Apothem x Side
What is the perimeter of hexagon?
The perimeter of a regular hexagon, whose side is s, is equal to 6s.
To know more than almost the other characteristics and attributes of polygons such as hexagon, pentagon, octagon and other geometrical figures download BYJU'S-The Learning App.
Source: https://byjus.com/maths/area-of-hexagon/
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