# The Area of a Polygonal Region

We know that there is a close analogy between the concept and properties of the area of a polygonal region and those of the length of a line segment. Here, we would like to express the concept of area in terms of the length of line segment(s).

**I. ****Area Axiom :-**

Every polygonal region has an area which is measured in 'square units'. The standard unit of area is 'square metre' i.e. area of a square whose sides are of one metre length. The area of a polygonal region in square metres (sq. m or m^{2}) is always a positive real number. Area also cannot be negative like length. The area of a polygonal region R is denoted by ar(R). If the area of a polygonal region R in square metres is x, then

ar(R) = x sq. m or x m^{2}.

**II. ****Congruent Area Axiom :-**

If two triangles Î” ABC and Î” DEF are congruent, their area will be equal and will be written as ar(region Î” ABC) = ar(region Î” DEF).

**III. ****Area Monotone Axiom :-**

If R_{1} and R_{2} are two polygonal regions such that R_{1}ÃŒ R_{2} then ar(R_{1}) â‰¤ ar(R_{2})

**IV. ****Area Addition Axiom :-**

If R_{1} and R_{2} are two polygonal regions, whose intersection is a finite number of points and line-segments, and R = R_{1}Ãˆ R_{2} then ar(R) = ar(R_{1}) + ar(R_{2})

**V. ****Area of a Rectangular Region :-**

Given that AB = a m and BC = b m, ar (Rectangular region ABCD) = a.b sq.m