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

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

Area = $\frac{s^2n}{4tan(\frac{180}{n})}$ where, the tangent function is always calculated in degrees.

Putting n = 10, we get the area of regular decagon with side length s as, Area = 7.6942 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}n tan($\frac{180}{n}$) where, n is the number of sides of a polygon.

Putting n = 10, we get the area of regular decagon with Apothem a, Area = 3.2492 a

^{2}.

**Case(iii)** When an 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 = 10, we get the area of regular decagon with radius r, Area = 2.9389 r

^{2}.

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

Area = 2.5ds where s is the side length.In case of an irregular Decagon, area can be found by breaking the decagon into 10 triangles and finding the area of each triangle and adding them up.