Question

Write True or False and justify your answer:

$PQRS$ is a parallelogram whose area is $180 \mathrm{~cm}^{2}$ and $A$ is any point on the diagonal $QS$. The area of $\triangle ASR$ is $90 \mathrm{~cm}^{2}$.

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Answer

:

False.

Given that the area of parallelogram $PQRS = 180 , \text{cm}^2$ and $QS$ is its diagonal which divides the parallelogram into two triangles of equal area.

So, the area of $\triangle SRQ = \frac{180}{2} = 90 , \text{cm}^2$.

Since $A$ is any point on the diagonal $QS$, the area of $\triangle ASR$ will be less than the area of $\triangle SRQ$.

Therefore, the area of $\triangle ASR$ cannot be $90 , \text{cm}^2$.


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