Question

In figure, $DE||BC,DE=3cm,BC=9cmandar\left(\Delta ADE\right)=30c{m}^2.Findarofquad.BCED.$

Answer 1

Since $DE\parallel BC,\angle D=\angle B$ and $\angle E=\angle C$ and

$\angle A$ remains the same.

So by AAA Criteria, we get

$△ABC\sim △ADE$

Since $\frac{DE}{BC}=\frac{1}{3}$

$\Rightarrow \frac{AD}{AB}=\frac{AE}{AC}=\frac{1}{3}$

So, $AB=3AD$ and $AC=3AE$

Now area of triangle $ABC=\frac{1}{2}\left(AB\right)\left(AC\right)=\frac{1}{2}\left(3AD\right)\left(3AE\right)=9\times \frac{1}{2}\left(AB\right)\left(AC\right)$

Area of $△ABC=\frac{1}{2}\left(AD\right)\left(AE\right))=9(30)=270c{m}^2$

Now, area of $BCDE=$ Area of $ABC-$ Area of $ADE=270-30=240c{m}^2$