In figure below, $DE\ ||\ BC$.
If $DE\ =\ 4\ m$, $BC\ =\ 6\ cm$ and $Area\ (ΔADE)\ =\ 16\ cm^2$, find the $Area\ of\ ΔABC$.
"
Given:
In the given figure $DE\ ||\ BC$.
$DE\ =\ 4\ m$, $BC\ =\ 6\ cm$ and $Area\ (ΔADE)\ =\ 16\ cm^2$.
To do:
We have to find the $Area\ of\ ΔABC$.
Solution:
In $ΔADE$ and $ΔABC$,
$\angle ADE = \angle ABC$ (Corresponding angles)
$\angle DAE = \angle BAC$ (Common)
Therefore,
$ΔADE ~ ΔABC$ (By AA Similarity)
We know that,
The ratio of areas of two similar triangles is equal to the ratio of squares of their corresponding sides.
Therefore,
$\frac{Ar(ΔADE)}{Ar(ΔABC)} = (\frac{DE}{BC})^2$
$\frac{16}{Ar(ΔABC)} = (\frac{4}{6})^2$
$Ar(ΔABC) = \frac{36 \times 16}{16}$
$Ar(ΔABC) = 36\ cm^2$
The $Area\ of\ ΔABC$ is $36\ cm^2$.
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