Area of Parallelograms and triangles - ESSENTIAL POINTS

• 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 equal areas but the opposite need not be true.
• 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 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 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. [b x h]
• Parallelograms on the same base (or equal bases) and between the same parallels are equal in area.
• 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 the area of the triangle is half of the area of the parallelogram.
• Area of a triangle is half the product of its base and the corresponding altitude. [ ½ b x h]
• Triangles on the same base (or equal bases) and between the same parallels are equal in area.
• Triangles on the same base (or equal bases) and having equal areas lie between the same parallels.
• A median of a triangle divides it into two triangles of equal areas.