In given figure $△$ ABC and $△$ DEF are similar, BC=3cm, EF=4cm, and area of triangle ABC=54 $c m^{2}$ find the area of $△$ DEF

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Solution

We know that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

So, $\frac{B C}{E F}$ = $\frac{a r e a o f Δ A B C}{a r e a o f △ D E F}$
$\Rightarrow \frac{3^{2}}{4^{2}}$ = $\frac{54}{a r e a o f △ D E F}$
$\Rightarrow \frac{9}{16}$ = $\frac{54}{a r e a o f △ D E F}$

Thus, area of $△$ DEF = 96 $c m^{2}$

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In given figure $△$ ABC and $△$ DEF are similar, BC=3cm, EF=4cm, and area of triangle ABC=54 $c m^{2}$ . Find the area of $△$ DEF. (Note: The given figures are not to scale.)

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In given figure △ ABC and △ DEF are similar, BC=3cm, EF=4cm, and area of triangle ABC=54cm2 find the area of △ DEF __

We know that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. So, BCEF =area of ΔABCarea of △DEF⇒3242 =54area of △DEF⇒916 =54area of △DEF Thus, area of △ DEF = 96cm2

In given figure $△$ ABC and $△$ DEF are similar, BC=3cm, EF=4cm, and area of triangle ABC=54 $c m^{2}$ find the area of $△$ DEF

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