What We Have Discussed

Area of a figure is a number (in some unit) associated with the part of the plane enclosed by that figure.

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

If X is a planer region formed by two non-overlappingoverlapping planer regions of figures P and Q, then ar(X) = ar(P) + ar(Q)

Two figures are said to be on the same base and between the same parallels, if they have a common base (side) and the vertices (or the vertex) opposite to the base of each figure lie on a line to the base.

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

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

Parallelogram on the same base (or equal bases) and having 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 the area of the parallelogram.

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

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