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In parallelogram $ABCD,$ $AB ‖ DC$ and area of parallelogram is $280 cm 2$ . Point $P$ and $Q$ divide $AB$ and $DC$ respectively in the ratio 2: 3. Find the area of the parallelogram APQD.

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130 c m 2

150 c m 2

122 c m 2

112 c m 2

answer is D.

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Detailed Solution

Given,
Area of parallelogram ABCD = 280cm2.
Question Image

Also point

P

and

Q

divide

AB

and

DC

respectively in the ratio 2: 3.

A P : A B = 2 : 3 ⇒ A P = 2 2 + 3 A B ⇒ A P = 25 A B

Area of parallelogram = base

\times

height

⇒ a r A P Q D = A P h ⇒ a r A P Q D = 25 A B h ⇒ a r A P Q D = 25280 ⇒ a r A P Q D = 112 c m 2

The area is

112 c m 2

.
Hence, the correct option is 4.

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