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In the figure, $D$ is the mid-point of side B C of $Δ ABC$ and $E$ is the mid-point of $AD$ , then find the area of $Δ ABE$ .

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a r Δ A B E = 14 Δ A B C

a r Δ A B E = 12 Δ A B C

a r Δ A B E = a r Δ A B C

a r Δ A B E = 13 Δ A B C

answer is A.

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Detailed Solution

Given that

D

is the mid-point of side BC of

Δ ABC

and

E

is the mid-point of

AD

Since AD is the median,

a r Δ A B D = 12 a r Δ A B C

[Median divides the triangle into two equal parts.]

a r Δ A B E = 12 a r Δ A B D

[BE is the median]

∴ a r Δ A B E = 12 12 a r Δ A B C ⇒ a r Δ A B E = 14 Δ A B C

The area is

a r Δ A B E = 14 Δ A B C

.
Hence, the correct option is 1.

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