In a ABC- D and E are the midpoints of AB and AC- DE is parallel to BC- If the area of - ABC - 60 sq cm- then the area of the - ADE is equal to-

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Area of Triangle Between Two Parallels

In a ABC, ...

Question

In a $△ A B C$ , $D$ and $E$ are the midpoints of $A B$ and $A C . D E$ is parallel to $B C$ . If the area of $Δ A B C = 60$ sq cm., then the area of the $Δ A D E$ is equal to:

15

sq. cm

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20

sq. cm

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25

sq. cm

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30

sq. cm

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Solution

The correct option is C $15$ sq. cm
Given, $D$ and $E$ are mid-points of $A B$ and $A C$ respectively.
$∴ \frac{A D}{A B} = \frac{1}{2}$
Now, $\frac{A r . (Δ A D E)}{A r . (Δ A B C)} = \frac{{A D}^{2}}{{A B}^{2}}$
$A (Δ A D E) = \frac{1}{4} \times 60 = 15 {c m}^{2}$
Hence, option A is correct.

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In a △ABC, D and E are the midpoints of AB and AC.DE is parallel to BC. If the area of ΔABC=60 sq cm., then the area of the ΔADE is equal to:

The correct option is C 15 sq. cmGiven, D and E are mid-points of AB and AC respectively.∴ADAB=12Now, Ar.(ΔADE)Ar.(ΔABC)=AD2AB2A(ΔADE)=14×60=15cm2Hence, option A is correct.

In a $△ A B C$ , $D$ and $E$ are the midpoints of $A B$ and $A C . D E$ is parallel to $B C$ . If the area of $Δ A B C = 60$ sq cm., then the area of the $Δ A D E$ is equal to:

The correct option is C $15$ sq. cm
Given, $D$ and $E$ are mid-points of $A B$ and $A C$ respectively.
$∴ \frac{A D}{A B} = \frac{1}{2}$
Now, $\frac{A r . (Δ A D E)}{A r . (Δ A B C)} = \frac{{A D}^{2}}{{A B}^{2}}$
$A (Δ A D E) = \frac{1}{4} \times 60 = 15 {c m}^{2}$
Hence, option A is correct.