The area of a Hexagon can be found in different ways. We can use various formulas depending on the data when the hexagon is regular.

**Case (i)** When the side length, s, is given the area of any n sided polygon is given by,

Area =

$\frac{s^{2}n}{4tan}$(

$\frac{180}{n}$), where the tangent function is always calculated in degrees.

Putting n = 6, we get the area of regular hexagon with side length s as, Area = 2.5981 s

^{2}.

**Case (ii)** When an Apothem ‘a’(Apothem of a regular polygon is a perpendicular line segment drawn from the center to the midpoint of

one of its sides) is given then the area of a polygon is given by :

Area = a

^{2}ntan(

$\frac{180}{n}$) where n is the number of sides of a polygon.

Putting n = 6, we get the area of regular hexagon with Apothem ‘a’, Area = 3.4641 a

^{2}.

**Case(iii)** When a Radius ‘r’(Radius of a regular polygon is a distance from the center to any of the vertex) is given, then the area of a polygon is given by

Area =(

$\frac{1}{2}$) r

^{2}nSin(

$\frac{360}{n}$) where n is the number of sides of a polygon.

Putting n = 6, we get the area of regular hexagon with radius r, Area = 2.5981 r

^{2}.

If r is the radius and A is the apothem, the area is also given by Area = ½ r ACase(iv) Alternatively in a regular Hexagon, if the distance between any two parallel sides or the height when the hexagon stands on one side as base is given as d, then the formula for area is given by:

Area = 1.5ds where s is the side length.

In case of an irregular Hexagon, area can be found by breaking the hexagon into 6 triangles and finding the area of each triangle and adding them up.