Question

PORS is a parallelogram. G is any point in the interior such that a, (OGR) = 6cm' and
Q-(APGS) = 10cm?. Find PQRS (Hint: Through G, draw LM || PS)​

Answer 1

Answer:

Let PQRS is a parallelogram. Let G be any point in its interior.

Through G, draw aline LM parallel to PS.

In quad. PMLS, we have

LM || PS and PM || SL

⇒quad. PMLS is a parallelogram.

In quad. QMLR, we have

LM || RQ and MQ || LR,

⇒ quad. QMLR is a parallelogram.

Since △ PGS and ||gm PMLS have common base PS and between same parallels LM and PS,

so, ar(||gm PMLS) = 2 ar (△PGS) = 2 (10) = 20 cm2 [as, ar (△PGS) = 10 cm2 ]

Since △ QGR and ||gm QMLR have common base QR and between same parallels LM and QR.

so, ar (||gm QMLR) = 2 ar (△QGR) = 2(6) = 12 cm2 [ as, ar (△QGR) = 6 cm2 ]

Now, ar(||gm PQRS) = ar(||gm PMLS) + (||gm QMLR) = 20 + 12 = 32 cm2

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student-nameAncella Martin answered this

37 helpful votes in Math, Class XII-Science

area of pqrs would be= 32sq.cm