Let $A B C D$ be a parallelogram of area $124 \mathrm{~cm}^{2}$. If $E$ and $F$ are the mid-points of sides $A B$ and $C D$ respectively, then find the area of parallelogram AEFD.
Given,
Area of a parallelogram $A B C D=124 \mathrm{~cm}^{2}$
Construction: Draw AP⊥DC
Proof:-
Area of a parallelogram AFED = DF × AP ⋅⋅⋅⋅⋅⋅⋅⋅ (1)
And area of parallelogram EBCF = FC × AP⋅⋅⋅⋅⋅⋅⋅⋅ (2)
And DF = FC ⋅⋅⋅⋅⋅ (3) [F is the midpoint of DC]
Compare equation (1), (2) and (3)
Area of parallelogram AEFD = Area of parallelogram EBCF
$\therefore$ Area of parallelogram $\mathrm{AEFD}=\frac{\text { Area of parallelogram } \mathrm{ABCD}}{2}=\frac{124}{2}=62 \mathrm{~cm}^{2}$
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