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Figures on the Same Base and between the Same Parallels

In a parallel...

Question

In a parallelogram ABCD, M is the midpoint of side CD. A point N is chosen on DC extended such that, CN = MC and MN || AB What is the ratio of Area(ABCD):Area(ABNM)?

3 : 1

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1 : 2

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1 : 1

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2 : 1

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Solution

The correct option is C 1 : 1
Given,
MC is $\frac{1}{2}$ of CD and CN = MC
$M N = M C + C N = \frac{C D}{2} + \frac{C D}{2} = C D$

As, it is given that MN || AB ,
$∴$ ABMN is a parallelogram.

Now since the ABCD and ABMN are parallelograms between the same parallel lines and equal base, they have the same area.

Therefore, the ratio of their areas is 1:1.

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