What are the basic properties of regular polygon with different number of sides?

Let us learn primary properties of regular polygon like rhombus, pentagon and octagon.

Properties of Kite

A kite is a regular polygon identified as rhombus. A rhombus is two disjoint pairs with consecutive sides congruent to each other. The diagonals are perpendicular to each other where one diagonal (main diagonal) bisect other diagonal (cross diagonal) making the pair of opposite angles.

Area of a kite (Rhombus) Area = (½) d1d2                            

where d1 and d2 long and short diagonals of kite

Properties of Pentagon 

Regular pentagon is the polygon with 5 sides where all the angles and sides are same. By cutting pentagon from the center of the pentagon to the center of each side forms 90⁰ angles on each side and length of each side exactly half of its original length. Hence, regular pentagon gives us bunch of right angled triangles. Firstly, we need to find out area of one triangle.               

Area of a Triangle = (½) * base * height

A pentagon comprises of 10 such triangles. Hence, multiply 10 with area of one triangle to find total area of a pentagon.

Area of a Pentagon formula = 10 * area of one triangle (that forms Pentagon)

Properties of Octagon

Octagon is another type of a regular polygon comprises of even number of sides with opposite sides are parallel to each other. Additionally, the sides and angles of octagon have same measure which makes it easy to find out area of a octagon.

Area of a Octagon formula Area = s^{2 *}(2 + 2(√2))                where s is the length of the side.

There is no such formula to find area of irregular polygon with different sides. It varies from case to case depending on the geometry of irregular polygon.