The area of a Heptagon can be found in different ways. We can use various formulas depending on the data when the heptagon 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 = 7, we get the area of regular heptagon with side length s as, Area = 3.633 s

^{2}.

**Case (ii)** When an Apothem ‘a’(Apothem of a regular polygon is a perpendicular line segment drawn from the centre 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 = 7, we get the area of regular heptagon with Apothem ‘a’, Area = 3.371 a

^{2}.

**Case(iii)** When a Radius ‘r’(Radius of a regular polygon is a distance from the centre 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 = 7, we get the area of regular heptagon with radius r, Area = 2.7364 r

^{2}.

If p is the Perimeter and A is the apothem, the area is also given by Area = ½ P AIn case of an irregular Heptagon, area can be found by breaking the heptagon into 7 triangles and finding the area of each triangle and adding them up.