The area of parallelogram ABCD is 36 cm². Calculate the height of parallelogram ABEF if AB = 4.2 cm.

Extend BA to H and drop a perpendicular from D on AH mark intersection point I as shown in the figure

DI is the height of parallelogram ABCD

Given base = AB = 4.2 cm

Area of parallelogram ABCD = 36 sq. cm

Area of parallelogram = base × height

⇒ Area of parallelogram ABCD = AB × DI

⇒ 36 = 4.2 × DI

⇒ DI = = = =

⇒ DI = 8.57 cm

Now as seen in the figure points E and F of the parallelogram ABEF lie on the same line as that of D and C

Therefore DE || AB

Perpendicular distance between parallel lines is constant

Therefore, for parallelogram ABEF the perpendicular distance between EF and AB will be DI i.e. 8.57 cm

Therefore, height of parallelogram ABEF is 8.57 cm