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.

Answer 1

ABCD be a parallelogram. 

Area of parallelogram = 124 cm² (Given) 

Consider a point P and join AP which is perpendicular to DC. 

Now, Area of parallelogram EBCF = FC x AP and 

Area of parallelogram AFED = DF x AP 

Since F is the mid-point of DC, so DF = FC 

From above results, we have 

Area of parallelogram AEFD = Area of parallelogram EBCF = 1/2 (Area of parallelogram ABCD) 

= 124/2 

= 62 

Area of parallelogram AEFD is 62 cm².