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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
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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