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Question
In the figure, AE = BE. Prove that the area of triangle ACE is equal in area to the parallelogram ABCD.
Solution
In parallelogram ABCD,
ar(ΔABC) = `(1)/(2)` x ar(parallelogram ABCD)
(The area of a triangle is half that of a parallelogram on the same base and between the same parallels)
ar(parallelogram ABCD) = 2ar(ΔABC) ........(i)
In ΔACE,
ar(ΔACE) = ar(ΔABC) + ar(ΔBCE)
but ar(ΔABC) = ar(ΔBCE) ...(since BC is median)
ar(ΔACE) = 2ar(ΔABC) .........(ii)
From (i) and (ii)
ar(parallelogram ABCD) = ar(ΔACE).
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