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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Solution

Given, $△ A B C$ is similar to $△ D E F$
And $B C = 3 c m, E F = 4 c m$
Area of $△ A B C = 54 c m^{2}$

Since the ratio fo areas of two similar triangles is equal to the ratio of the squares of any two corresponding sides.

$\Rightarrow$ $\frac{A r e a (△ A B C)}{A r e a (△ D E F)} = \frac{(B C)^{2}}{(E F)^{2}}$

$\Rightarrow$ $\frac{54}{A r e a (△ D E F)} = \frac{3^{2}}{4^{2}}$

$\Rightarrow$ Area ( $△$ DEF) = $\frac{54 \times 16}{9}$ = 96 $c m^{2}$

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Similar questions

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 .

Q. If

△ A B C

is similar to

△ D E F

such that

B C = 3

cm,

E F = 4

cm and area of

△ A B C = 54 {cm}^{2} .

Find the area of

△ D E F .

(in cm

^{2}

)

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.)

c m^{2}

In the given figure, $△ A B C$ and $△ D E F$ are similar. BC = 3 cm, EF = 2 cm, and area of $△ A B C = 54 c m^{2}$ , then the area of $△ D E F$ is __ $c m^{2} .$

△ A B C \sim △ D E F

. IF

B C = 4 c m

E F = 5 c m

and area

(△ A B C) = 32 {c m}^{2}

, determine the area of

△ D E F

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If △ABC is similar to △DEF such that BC = 3 cm, EF = 4 cm and area of △ABC = 54 cm2. Determine the area of △DEF.

Given, △ABC is similar to △DEFAnd BC=3 cm,EF=4 cmArea of △ABC=54 cm2Since the ratio fo areas of two similar triangles is equal to the ratio of the squares of any two corresponding sides. ⇒ Area (△ABC)Area (△DEF)=(BC)2(EF)2 ⇒ 54Area (△DEF)=3242 ⇒ Area (△ DEF) = 54×169 = 96 cm2

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.