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Question
If a triangle and a parallelogram lie on the same base and between the same parallels, then prove that the area of the triangle is equal to half of the area of parallelogram
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Solution
Let ΔAPB and parallelogram ABCD lie on base AB and between parallels AB and PC.
To show area ΔAPB = `1/2` Area (ABCD)
Now, draw BQ || AP.
Then ABQP is a parallelogram.
Now area ABQP = Area ABCD .....(They are on same base AB and between same parallels AB and PC)
⇒ ΔPAB ≅ ΔBQP
Area PAB = Area BQP
= `1/2` Area ABQP
= `1/2` Area ABCD
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