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  • Write true or false and justify your answer. PQRS is a parallelogram whose area is 180 cm^2 and A is any point on the diagonal QS. The area of DASR = 90 cm^2.

Write true or false and justify your answer.
PQRS is a parallelogram whose area is 180 cm2 and A is any point on the diagonal QS. The area of DASR = 90 cm2.

Answers (1)

best_answer

Answer: [False]

Solution.

Given, PQRS is a parallelogram whose area is 180cm^{2}

We know that diagonal of a parallelogram divides it into two triangles of equals area, so
\therefore ar(\triangle QRS)=\frac{1}{2}ar(\parallel gmPQRS)
                           =\frac{1}{2}\times 180=90cm^{2}
 

Given that A is any point on SQ
So, ar (\triangle ASR) < ar(\triangle QRS)
Hence,ar (\triangle ASR) < 90 cm^{2}
But given that area of \triangle ASR = 90 cm^{2}

Hence, the given statement is false. 

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