In the given figure A B C D and A B F E are parallelograms such t… - Vidyadip

MCQ

In the given figure $A B C D$ and $A B F E$ are parallelograms such that ar(quadrilateral $E A B C)=17 \mathrm{~cm}^2$ and $\operatorname{ar}(\| \mathrm{gm} A B C D)=$ $25 \mathrm{~cm}^2$. Then, $\operatorname{ar}(\triangle \mathrm{BCF})=$ ?

A
$4 \mathrm{~cm}^2$
B
$4.8 \mathrm{~cm}^2$
C
$6 \mathrm{~cm}^2$
✓
$8 \mathrm{~cm}^2$

✓

Answer

Correct option: D.

$8 \mathrm{~cm}^2$

From the given figure, we have $||\ gm\ ABCD$ and $||\ gm\ ABFE$ are lying on the same base and between the same parallels.
$\Rightarrow\ \text{ar}(||\text{gm ABCD})=\text{ar}(||\text{gm ABFE})=25\text{cm}^2$
$\Rightarrow\ \text{ar}(\triangle\text{BCF})=\text{ar}(||\text{gm ABFE})-\text{ar(quadrilateral EABC)}$
$=25-17$
$=8\text{cm}^2$

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