Areas of Parallelograms and Triangles

If two figures are congruent, then they have equal areas. However, the converse of this statement is not true. If a planar region formed by a figure T is made up of two non-overlapping planer regions formed by figures P and Q, then area(T) = area(P) + area(Q). Two figures are said to be on the same base and between the same parallels, if they have a common base and the vertex opposite to the common base of each figure lie on a line parallel to the base. Area of a parallelogram is the product of its base and the corresponding altitude. Area of a triangle is half the product of its base and the corresponding altitude. A median of a triangle divides it into two triangles of equal areas. Parallelograms on the same base and between the same parallels are equal in area. Parallelograms on the same base and having equal areas lie between the same parallels. Triangles on the same base and between the same parallels are equal in area. Two triangles having same base (or equal bases) and equal areas lie between the same parallels. Area of a triangle is half the area of the parallelogram, if the triangle and the parallelogram are on equal bases and between the same parallels.

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