ABCD and ABFE are parallelograms as shown in the figure. If ar (ABCD) = 36 cm2 and ar(ABFE) = 18 cm2, then ar (EFCD) [in cm2] is
Join BP as shown in the figure.
Since ADCB and DQPC lie on the same base DC and are between the same parallels AP and DC,
∴Area (ADCB) = Area (DQPC) = 36 cm2.. (1)
Again, AEBF and EFPQ lie on the same base EF and are between the same parallels EF and AP.
∴ Area (ABEF) = Area (EFPQ) ... (2)
On adding equations (1) and (2), we obtain
Area (DCEF) = Area (DQPC + Area (EFPQ) = 54 cm2