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What is the area of the parallelogram PQTU if the area of the parallelogram PQRS is 100 cm²?

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50 cm²

$50 \sqrt{2}$ cm²

100 cm²

$100 \sqrt{2}$ cm²

answer is C.

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Detailed Solution

The quadrilaterals PQTU and PQRS are parallelogram.

∴PQ||RS and PQ||TU

⇒ PQ||RU

∴The parallelograms PQTU and PQRS are on the same base and between the same parallels because they have a common base PQ and the vertices opposite to the common base PQ of each figure lie on a line RU which is parallel to the base.

We know that, parallelograms on the same base and between the same parallels are equal in area.

∴ Area of parallelogram PQRS = area of parallelogram PQTU

It is given that, area of the parallelogram PQRS = 100 cm²

∴ Area of parallelogram PQTU = 100 cm².

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