Question

What’s the area formula for a hexagon?

Answer 1

Hint: From the question given we have to write the formula for the area of a hexagon. As we know that the hexagon contains six sides and six angles. To find the area we will split the regular hexagon into six equilateral triangles then the sum of all the areas of an equilateral triangle is equal to the area of a regular hexagon.

Complete step-by-step answer:
Hexagon: 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 we are 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 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.
In a regular hexagon, split the figure into triangles which are equilateral triangles
Find the area of one triangle
Multiply the value by six.
One of the easiest methods that can be used to find the area of a polygon is to split the figure into triangles. splitting the hexagon into six triangles

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 triangles 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
We know that the formula of area of equilateral triangle having sides is
$= \dfrac{\sqrt{3}}{4}{{s}^{2}}$
Now, we have six equilateral triangles in a regular hexagon so we will multiply with six to the area of equilateral triangle,
 Area of hexagon will be
 $= 6\times \dfrac{\sqrt{3}}{4}{{s}^{2}}$
$= \dfrac{3\sqrt{3}}{2}{{s}^{2}}$
Therefore, the area of the hexagon is $\dfrac{3\sqrt{3}}{2}{{s}^{2}}$ where s is the side of a regular hexagon.

Note: Students should also know that the another formula for area of hexagon is, we divide the hexagon into two isosceles triangles and one rectangle then we can show that the area of the isosceles triangles are $\dfrac{1}{4}th$ of the rectangle whose area is $s\times h$, So, area of regular Hexagon formula is given by
$= \dfrac{3}{2}\times s\times h$
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.