Question

$ABCD$ and $BCFE$ are parallelograms. If area of $△EBC=960c{m}^2$; $AB=30$ cm and $BC=40$ cm; Calculate area of the parallelogram $BCFE$:

• A. $1920c{m}^2$
• B. $960c{m}^2$
• C. $1360c{m}^2$
• D. None of these

Answer 1

The correct option is A $1920c{m}^2$

ABCD and BCFE are parallelograms.
Area of $△EBC=960c{m}^2$
$AB=30$ cm
$BC=40$ cm
Now, let $E{E}^{\prime }$ be a altitude from $E$ to base $E{E}^{\prime }$
$\therefore$ Area of $△EBC=\frac{1}{2}BC\times E{E}^{\prime }$
$\Rightarrow 960=\frac{1}{2}40\times E{E}^{\prime }$
$\Rightarrow E{E}^{\prime }=\frac{96}{2}$
$\Rightarrow E{E}^{\prime }=48$ cm
Area of parallelogram ABCD=$BC\times$ height
$=$ $BC\times E{E}^{\prime }$
$=$ $40\times 48$
$=$ $1920c{m}^2$
Area of parallelogram $BCFE=$ Area of parallelogram $ABCD$
Similarly, both parallelogram are on the same base and between the same parallels.
$\therefore$ Area of parallelogram $BCFE=$ $1920c{m}^2$