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Areas > Area of Planar Regions

Area of Planar Regions

Below we can see different types of planar figure:

Often, a planar figure can be made up of two or more simpler planar regions. The area of a composite figure equals the sum of the areas of its parts. We can write this as:

Area of figure = Ar.(A) + Ar.(B) + Ar.(C)

Keeping this in mind, we can express the following areas as:

Area = Ar. of + × Ar. of

Area = Ar. of + × Ar. of

Area = Ar. of + × Ar. of

(a) Congruent Figures

When two figures are congruent (exactly the same shape and size), their areas are . If figures A and B are congruent, then area(A) = area(B)

(b) Sum of Parts

The area of any figure equals the of the areas of its non-overlapping parts For instance, if figure X is divided into non-overlapping regions P and Q, then area(X) = area(P) + area(Q)