Area of a hexagon can be found by using two formulas which are mentioned in this article in detail. Read out the article to understand more about the area of hexagon formula.
A hexagon is a polygon which contains 6 sides as its name suggests the is derived from Greek words that are “Hexa” the meaning of which is six and “gonia” the meaning of which is corners. In a combined way that is called a six corners polygon. Here, all the sides and corners/angles are equal. And the angles have a value of 120 degrees.
Area of Hexagon
As we all know that the area is the region enclosed in the particular polygon, here in the case of the hexagon is also the same. A hexagon is a polynomial having 6 sides, 6 angles and 9 diagonals. Moreover the sum of all angles comes out to be 720 degrees. The units for measurement of area of a hexagon are m2, cm2, mm2, ft2, inch2, etc. in whichever units it is required, the unit is squared and we get the unit of its area.
The formula for the area of a hexagon can be written as,
s = side of the hexagon given.
Derivation of Area of Hexagon
After we got to know the formula for the area of a hexagon, we are curious to know how that particular formula is derived. So, let us derive the same.
The first step in deriving the formula for a regular hexagon is drawing the same in a sheet of paper as shown below,
Now, that we’ve drawn a hexagon, we need to divide it into 6 equal triangular parts as shown below,
Also, annotate the height of the triangle and side as shown.
As we all know the basic formula for area of a triangle which is ,
Substituting the values as
b = s (side of hexagon)
And h = h (height of the triangle formed in the hexagon)
Now, since, we have 6 similar triangles inside a hexagon. Thus, the area of the hexagon becomes equal to 6 times the area of one triangle into the hexagon. Mathematically depicting the same as,
Now, we need to find the value of h using pythagoras theorem,
And at the end when we apply the same value of h in the formula of hexagon obtained we get the equation as,
Area of a Hexagon Using Apothem
Sometimes the radius of the hexagon is also given, and we can also get another formula using the same. Here the radius of the hexagon is called the apothem. We can also understand it by taking it as the height of one triangle inside the hexagon.
The formula for the area of a hexagon using apothem is as,
And the perimeter of the hexagon can be found out by
Find the area of a hexagon having side of 10 cm
For that we simply use the formula,
And substitute the value of s which is equals to 10 cm