Question

the sides AS of a parallelogram ABCD is produced to any point P.a line through A and parallel toCP meet CB produced at Q and then parallelogram PBQR is completed.show that Ar(ABCD= Ar(PBQR).​

Answer 1

Explanation:

PBQR is completed. Show that ar(ABCD)=ar(PBQR).

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Answer

Let us join AC and PQ.

△ACQ and △AQP are on the same base AQ and between the same parallels AQ and CP.

∴ Area (△ACQ)= Area

(△APQ)

⇒ Area(△ACQ)−Area(△ABQ)= Area(△ACQ)−Area(△ABQ)

⇒ Area (△ABC)= Area (△ABQ) ... (1)

Since AC and PQ are diagonals of parallelograms ABCD and PBQR respectively,

∴ Area (△ABC)=

2

1

Area of parallelogram ABCD ... (2)

Area(△QBP)=

2

1

Area of parallelogram BPRQ ... (3)

From equations (1),(2), and (3), we obtain

2

1

Area of parallelogram ABCD=

2

1

Area of parallelogram BPRQ

∴ Area of parallelogram ABCD= Area of parallelogram