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In $Δ A B C$ , D and E are the midpoints of AB and AC respectively, then the area of $Δ A D E$ is

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4 ×

Area of

Δ A B C

14 ×

Area of

Δ A B C

2 ×

Area of

Δ A B C

12 ×

Area of

Δ A B C

answer is B.

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Detailed Solution

Since D and E are the midpoints of AB and AC.
Draw a triangle ABC with D and E as midpoints AB and AC.
Since D is the midpoint of AB, this means that AB will be twice AD.

∴ 2 A D = A B → e q n .1

Similarly, E is the midpoint of AC , it means AC will be twice of AE.

∴ 2 A E = A C → e q n .2

Now , we know Area of triangle =

12 × b a s e × h e i g h t

So, Area of

Δ A B C = 12 × A C × A B

Since, ADE also from a triangle

12 × A E × A D

From eqn. 1 and eqn. 2 , we get

= 12 × A C 2 × A B 2 ​ = 12 × 12 × A C × A B ​ = 14 (area of Δ A B C)

So, the correct answer is Option 2.

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In ΔABC , D and E are the midpoints of AB and AC respectively, then the area of ΔADE is

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In $Δ A B C$ , D and E are the midpoints of AB and AC respectively, then the area of $Δ A D E$ is