AREAS OF PARALLELOGRAMS AND TRIANGLES

AREAS  OF PARALLELOGRAMS AND TRIANGLES

SOME IMPORTANT POINTS TO REMEMBER

·      Two figures are called congruent, if they have the same shape and the same size.

·      Area of a figure is a number(in some unit) associated with the part of the plane enclosed by the figure with following two properties:

                                                        i.            If  A and B are two congruent figures, then ar (A) = ar (B).

                                                      ii.            If a planar region formed by a figure T is made up of two non-overlapping  planar regions formed by figures P and Q , then ar(T)= ar (P) + ar(Q).

·      Two congruent figures have equal areas but the converse need not be true.

·      Parallelograms on the same base(or equal bases) and between the same parallels are equal in area.

·      Area of a parallelogram is the product of its base and the corresponding altitude.

·      Parallelograms on the same base(or equal bases) and having equal areas lie between the same parallels.

·      If a parallelogram and a triangle are on the same base and between the same parallels, then area of the triangle is half the area of the parallelogram.

·      Triangles on the same base(or equal bases) and between the same parallels are equal in area.

·      Area of a triangle is half the product of its base and the corresponding  altitude.

·      Triangles  on the same base(or equal bases) and having equal areas lie between the same parallels.

·      A median of a triangle divides it two triangles equal areas.