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Question

The given figure shows parallelogram ABCD. Points P and Q trisect the side AB, then which of the following is correct?


A
Area of DPQ = 13 Area of (parallelogram ABCD)
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B
Area of DPQ = 25 Area of (parallelogram ABCD)
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C
Area of DPQ = 16 Area of (parallelogram ABCD)
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D
Area of DPQ = 45 Area of (parallelogram ABCD)
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Solution

The correct option is C Area of DPQ = 16 Area of (parallelogram ABCD)

We know that triangles between same parallels and on the same base have half the area of the parallelogram.
So, Area of DQC=12 (area of parallelogram ABCD )
Let 'h' be the height between the parallel lines.
PQ=13AB (P and Q trisects AB)
Hence, Area of DPQ=12×13×AB×h
Area of DPQ=16(area of parallelogram ABCD)


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