# Let ABCD be a parallelogram of area 124 cm2.

Question:

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.

Solution:

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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