Let ABCD be a parallelogram of area 124 cm2. If E and F are the mid-points of sides AB and

CD respectively, then find the area of parallelogram AEFD.

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#### Solution

Given,

Area of parallelogram `ABCD = 124cm^2`

Construction: draw AP ⊥ DC

Proof :

Area of 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

∴ Area of parallelogram ABCD = `" Area of parallelogram"/"2"`

` = 124 / 2 = 62cm^2`

Concept: Concept of Area

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