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

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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.
$\frac{a r e a o f (△ A B C)}{a r e a o f (△ D E F)} = \frac{B C^{2}}{E F^{2}} = \frac{3^{2}}{4^{2}} = \frac{9}{16}$

On substituting the values we get:

$\frac{9}{16}$ = $\frac{54}{a r e a o f △ D E F}$

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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If $△$ ABC is similar to $△$ DEF such that BC = 3 cm, EF = 4 cm and area of $△$ ABC = 54 ${c m}^{2}$ . Determine the area of $△$ DEF.

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In given figure △ ABC and △ DEF are similar, BC = 3cm, EF = 4cm, and area of triangle ABC = 54cm2. The area of △ DEF is ___ cm2.

We know that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. area of (△ABC)area of (△DEF)=BC2EF2=3242=916 On substituting the values we get: 916 =54area of △DEF area of △ DEF = 96cm2

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