In the given figure, ABDE and BCDE are parallelograms and EF ⊥ AB and BG ⊥ CD. If AB = 4 cm, EF = 6 cm and CD = 8 cm, then what is the measure of BG?

Parallelograms on the same base and between the same parallels are equal in area.

∴Area (ABDE) = area (BCDE)

⇒ AB × EF = CD × BG

⇒ 4 cm × 6 cm = 8 cm × BG

⇒ BG = $\frac{24}{8}$ cm

⇒ BG = 3 cm