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In the given figure, D is the mid-point of side BC of $Δ ABC$ and E is the mid-point of AC. If $ar (DEC) = 6 sq .$ units, then $ar (ABC)$ (in sq. units) is equal to:

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answer is C.

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Detailed Solution

It is given that D and E are midpoints of BC and AC.
Also, area of

Δ

DEC = 6 units
Question Image

Let F be midpoint of AB, then, join DF and FE.
So, totally there formed four equal triangles inside triangle ABC.
Now, area of

Δ

ABC = 4

×

area of

Δ

DEC

\Rightarrow

Area of

Δ

ABC = 4

× 6

\Rightarrow

Area of

Δ

ABC = 24 units
So, if in triangle

Δ

ABC, area of

Δ

DEC = 6 units, then area of

Δ

ABC = 24 units.
Hence, the correct option is 3.

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