In the given figure, BCED is a parallelogram. CE is extended to the point A such that E is the midpoint of AC. The ratio of area $Δ D B C$ : area $Δ A B C$ is equal to ______.

1 : 1

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1 : 2

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2 : 1

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1 : 3

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Solution

The correct option is B 1 : 2

DE || BC (given)
Area of $Δ D B C$ = area $Δ E B C$ .... (triangles on the same base and between same parallels are equal in area) ------- (i)

EB is median of $Δ A B C$ .... (E is the midpoint of AC)
Area of $Δ A B C = 2 \times$ area $Δ E B C$ .... (median divides a triangles into two triangles of equal area )

$\Rightarrow Δ A B C = 2 \times$ area $Δ D B C$ ...... From (i)
$∴$ area $Δ D B C$ : area $Δ A B C = 1 : 2$

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In the given figure, BCED is a parallelogram. CE is extended to the point A such that E is the midpoint of AC. The ratio of area Δ DBC: area Δ ABC is equal to ______.

In the given figure, BCED is a parallelogram. CE is extended to the point A such that E is the midpoint of AC. The ratio of area $Δ D B C$ : area $Δ A B C$ is equal to ______.