Question

If a triangle and a parallelogram are on the same base and between the same parallels, then prove that the area of the triangle is equal to half the area of the parallelogram

Answer 1

Given:A parallelogram ABCD and ABP on the same base AB and between the same parallels PC & AB.
To prove: Area of triangle is equal to half the area of parallelogram. ar ( ABP ) = 1/2 ar (ABCD).
Proof: In parallelogram ABCD, AB CD So, PC AB We draw a line BQ parallel to AP , i.e. , BQ AP Since BQ AP & PQ AB, Both pairs of opposite sides are parallel ABQP is a parallelogram.
Parallelograms ABQP & ABCD are on the same base AB and between the same parallel lines AB & PC Area(ABQP) = Area(ABCD) In parallelogram ABQP, BP is the diagonal So, ABP QBP Area( ABP) = Area( QBP) Now, Area( ABP) = Area( QBP) = 1/2 Area(ABQP) Area( ABP) = 1/2 Area(ABQP) Area( ABP) = 1/2 Area(ABCD).
Hence proved.

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Answer 2

Answer:

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