Question

ABCD and ABFE are parallelograms as shown in the figure. If ar (ABCD) = 36 $c{m}^2$ and ar(ABFE) = 18 $c{m}^2$, then ar (EFCD) [in $c{m}^2$] is:

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Answer 1

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,

$\therefore$Area (ADCB) = Area (DQPC) = 36 $c{m}^2$.. (1)

Again, AEBF and EFPQ lie on the same base EF and are between the same parallels EF and AP.

$\therefore$ Area (ABEF) = Area (EFPQ) ... (2)

On adding equations (1) and (2), we obtain

Area (DCEF) = Area (DQPC) + Area (EFPQ) = 54 $c{m}^2$