Given $\vartriangle ABC\ \sim\vartriangle PQR$, If $\frac{AB}{PQ}=\frac{1}{3}$, then find $\frac{ar( \vartriangle ABC)}{ar( \vartriangle PQR)}$.
Given:$\vartriangle ABC\sim\vartriangle PQR$, and $\frac{AB}{PQ}=\frac{1}{3}$.
To do: $\frac{ar( \vartriangle ABC)}{ar( \vartriangle PQR)}=?$.
Solution:
$\vartriangle ABC\sim\vartriangle PQR$,
$ ( \because Ratio\ of\ area\ of\ similar\ triangle\ is\ equal\ to\ square\ of\ their\ proportional\ sides)$
$\frac{ar( \vartriangle ABC)}{ar( \vartriangle PQR)}=( \frac{AB}{PQ})^{2}$
$=( \frac{1}{3})^{2}$
$=\frac{1}{9}$
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