Question

ABCD is a parallelogram. If E and F are mid points of sides AB and CD and diagonal AC is joined, then ar(FCBE) : ar (CAB) is :

• A. $1:2$
• B. $2:1$
• C. $1:1$
• D. $1:4$

Answer 1

Answer: (C)

$1:1$

Point E and F are the mid points of AB and DC.

$\therefore ar\left(FCBE\right)=\frac{1}{2}ar\left(ABCD\right)⟶\left(1\right)$

$△ABC$ and parallelogram ABCD are on the same base and lie between the same parallel AD $\xi$ BC

$\therefore ar\left(ABC\right)=\frac{1}{2}ar\left(ABCD\right)⟶\left(2\right)$

From $\left(1\right)$ and $\left(2\right)$

$\therefore ar\left(FCBE\right)=ar\left(ABC\right)$

$\Rightarrow \frac{ar\left(FCBE\right)}{ar\left(ABC\right)}=1$

$\therefore$ The ratio is $1:1.$

Hence, the answer is $1:1.$