A farmer has distributed his field in the shape of parallelogram ABCD amongst his son and daughter according to the given figure Ar (BEC) of the land was given to the son and combined lands comprising of ar(AEB) ar(DEC) to his daughter.
Is the distribution of land between son and daughter are equal? Justify your answer.

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Solution

Let the base of parallelogram be $b$
And the height is $h$
The area of parallelogram is $b \times h = b h$
The area of triangle $B E C$ is $\frac{1}{2} \times b \times h = \frac{b h}{2}$
The remaining portion is given to daughter $b h - \frac{b h}{2} = \frac{b h}{2}$
So the areas are equal.

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Let the base of parallelogram be b And the height is hThe area of parallelogram is b×h=bhThe area of triangle BEC is 12×b×h=bh2The remaining portion is given to daughter bh−bh2=bh2So the areas are equal.

Let the base of parallelogram be $b$
And the height is $h$
The area of parallelogram is $b \times h = b h$
The area of triangle $B E C$ is $\frac{1}{2} \times b \times h = \frac{b h}{2}$
The remaining portion is given to daughter $b h - \frac{b h}{2} = \frac{b h}{2}$
So the areas are equal.