Question

In the given figure,ABCD and ABFE are parallelograms scuh that ar(quad.EABC)=$17c{m}^2$ and ar(||gm ABCD)=$25c{m}^2$.Then,ar($△BCF$)=?

(a) $4c{m}^2$

(b) $4.8c{m}^2$

(c) $6c{m}^2$

(d) $8c{m}^2$

Answer 1

(d) $8c{m}^2$

Since ||gm ABCD and ||gm ABFE are on the same base and between the same parallel lines, we have:
ar(||gm ABFE) = ar(||gm ABCD) = 25 cm
⇒ ar(∆BCF ) = ar(||gm ABFE) - ar(quad EABC) = ( 25 - 17) = $8c{m}^2$