Question

$ABCD$ and $BCFE$ are parallelograms. If area of triangle $EBC=480c{m}^2$, $AB=30cm$ and $BC=40cm$; Calculate;
(i) Area of parallelogram $ABCD$;
(ii) Area of the parallelogram $BCFE$;
(iii) Length of altitude from $A$ on $CD$;
(iv) Area of triangle $ECF$.

Answer 1

We have,

$\Delta EBC$ and parallelogram $ABCD$ are on the same base $BC$ and between the sme parallel $AD$ and $BC$.

Part (1):-

Then, we know that,

$ar\left(ABCD\right)=2\times ar\left(EBC\right)$

$=2\times 480$

$=960sq.cm.$

$ar\left(ABCD\right)=960sq.cm.$

Part (2):-

According to given Figure,

$ar\left(ABCD\right)=ar\left(BCEF\right)$

$ar\left(BCEF\right)=960sq.cm.$

Part (3):-

Length of altitude from point $A$ to $CD$

$AD=BC=40cm.$

Part (4):-

$ar\Delta \left(ECF\right)=ar\Delta \left(BEC\right)=480sq.cm.$

$ar\Delta \left(ECF\right)=480sq.cm$

Hence, this is the answer