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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 Δ ABC and Δ DEF are congruent, their area will be equal and will be written as ar(region Δ ABC) = ar(region Δ DEF).

III. Area Monotone Axiom :-
If R1 and R2 are two polygonal regions such that R1Ì R2 then ar(R1) ar(R2)

IV. Area Addition Axiom :-
If R1 and R2 are two polygonal regions, whose intersection is a finite number of points and line-segments, and R = R1È R2 then ar(R) = ar(R1) + ar(R2)

V. Area of a Rectangular Region :-
Given that AB = a m and BC = b m, ar (Rectangular region ABCD) = a.b sq.m





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