Mathematics
Bansidhar is a farmer. He has a field in the form of a parallelogram ABCD. He took any point P on CD and joined it to points A and B. In how many parts the field is divided? What are the shapes of these parts? Bansidhar gave the three parts of the field to his two sons equally. How did he do it?
Theorems on Area
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Answer
If a triangle and a parallelogram are on the same base and between the same parallels, then the area of the triangle is equal to half the area of the parallelogram.
△ ABP and parallelogram ABCD both share the base AB and lie between the same parallel lines, AB and CD.
Area (△ ABP) = Area(∥gm ABCD).
Son 1: Received the area of △ ABP.
Since the total area of the field is the sum of the three triangles, and one triangle takes up exactly half, the other two triangles must together make up the remaining half.
Son 2: Received the combined area of △ ADP and △ BCP
Hence, son 1 received the area of △ ABP and son 2 received the area of △ ADP and △ BCP.
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