# 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 m2) 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 m2.

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 R1 and R2 are two polygonal regions such that R1ÃŒ R2 then ar(R1) â‰¤ ar(R2)