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Question

If D, E, F are respectively the mid-points of the sides BC, CA, and AB of ABC, and the area of ABC is 24 cm2, then find the area of DEF.


A

24 cm2

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B

12 cm2

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C

8 cm2

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D

6 cm2

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Solution

The correct option is D

6 cm2


Given: D, E, and F are the mid-points of sides BC, AC, and AB respectively of ΔABC.

We know that DE = 12 (AB) (using mid-point theorem)

Similarly, FE = 12 (BC)
and FD = 12 (AC)

ΔABC will be similar to ΔDEF (by SSS similarity criterion)

Area (ΔDEF)Area (ΔABC)=(DEAB)2

Area ΔDEFArea ΔABC=(DE2 DE)2

Clearly, ar(DEF) = 14× ar(ABC)

= (14×24) = 6 cm2

Ar( DEF)= 6cm2


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