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Area of parallelogram and triangle Theorems

1) Area of a figure is a number with some unit associated with the part of the plane enclosed by that figure. Different types of figures have different areas. We have different formulas for finding area of some particular figures.

2) Two figures are called congruent, if they have the same shape and the same size. And two congruent figures have equal areas but the converse need not be true.

3) If A and B are two congruent figures, then area(A) = area(B);

and 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 area(T) = area(P) + area(Q).

4) Two figures are said to be on the same base and between the same parallels, if they have a common base or a side and the vertices or the vertex opposite to the common base of each figure lie on a line parallel to the base.In the above figure parallelogram ABCD and triangle ABE are on the same base and between the same parallels.

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

In the above figure parallelogram ABCD and ABEF are on the same base and between the same parallels, so they have equal areas.

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

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

8) 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.

In the above figure parallelogram ABCD and triangle ABE are on the same base and between the same parallels, so area of the triangle will be half the area of the parallelogram.

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

In the above figure triangle ABC and BCP are on the same base and between the same parallels, so area of both triangles will be equal.

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

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

12) A median of a triangle divides it into two triangles of equal areas.

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