ABCD is a parallelogram, DE is perpendicular to AB and DF is perpendicular to BC. If AB = 20 cm, BC = 10 cm and DF = 9 cm, then find DE.

Given, DF is perpendicular to BC

Taking BC as a base, BC = 10 cm 

 Height DF = 9 cm

Area of parallelogram ABCD = base x height

                       = 10 x 9

                       = 90 cm²      ... (eq. 1)

DE is perpendicular to AB

Taking AB as a base, AB = 20 cm

height is DE

Area of parallelogram ABCD = base x height

                                                   = 20 x DE    ... (eq. 2)

From eq. 1 and eq. 2,

90 = 20 x DE

DE = $\frac{90}{20}$ = 4.5 cm