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Question
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`
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