Question:
In the given figure ABCD and ABFE are parallelograms such that ar(quad. EABC) = 17 cm2 and ar(||gm ABCD) = 25 cm2. Then, ar(∆BCF) = ?
(a) $4 \mathrm{~cm}^{2}$
(b) $4.8 \mathrm{~cm}^{2}$
(c) $6 \mathrm{~cm}^{2}$
(d) $8 \mathrm{~cm}^{2}$
Solution:
(d) $8 \mathrm{~cm}^{2}$
Since ||gm ABCD and ||gm ABFE are on the same base and between the same parallel lines, we have:
$\operatorname{ar}(\| g m A B F E)=\operatorname{ar}(\| g m A B C D)=25 \mathrm{~cm}^{2}$
$\Rightarrow \operatorname{ar}(\Delta B C F)=\operatorname{ar}(\| \operatorname{gm} A B F E)-\operatorname{ar}($ quad $E A B C)=(25-17)=8 \mathrm{~cm}^{2}$
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