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Question

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


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Solution

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


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