Question

In the figure, AE = BE. Prove that the area of triangle ACE is equal in area to the parallelogram ABCD.

Answer 1

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).