Question

In the given, $△ABC~△DEF$. If $AB=2DE$ and the area of $△ABC\text{is}56$ sq.cm, find the area of $△DEF$.

Answer 1

Find the area of $△DEF$:

Given that,

$△ABC~△DEF$

$AB=2DE$ or $\frac{AB}{DE}=2$

$△ABC=56{\text{cm}}^2$

We know that the ratio of area of two similar triangles is equal to the squares of the ratio of corresponding sides.

$\therefore \frac{\text{Area of}△ABC}{\text{Area of}△DEF}=\frac{A{B}^2}{D{E}^2}$

Substitute the values we get,

$\Rightarrow \frac{56}{\text{Area of}△DEF}={\left(\frac{AB}{DE}\right)}^2$

$\Rightarrow \frac{56}{\text{Area of}△DEF}={\left(2\right)}^2$ [Since $\frac{AB}{DE}=2$]

$$\begin{gathered} \Rightarrow \text{Area of}△DEF=\frac{56}{4} \\ \Rightarrow \text{Area of}△DEF=14{\text{cm}}^2 \end{gathered}$$

Therefore, the area of $△DEF$ is $14$ sq.cm.