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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. - Mathematics

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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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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RD Sharma Mathematics for Class 9
Chapter 14 Areas of Parallelograms and Triangles
Exercise 14.2 | Q 3 | Page 15
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