PQRS is a square. If PR = 10 , cm,then the ar | vedclass

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(B) Let the side of the square $PQRS$ be $a \, cm$.In a square,the diagonal $d$ is related to the side $a$ by the formula $d = a\sqrt{2}$.Given that t

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$50$

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(B) Let the side of the square $PQRS$ be $a \, cm$.In a square,the diagonal $d$ is related to the side $a$ by the formula $d = a\sqrt{2}$.Given that the diagonal $PR = 10 \, cm$,we have $a\sqrt{2} = 10$.Solving for $a$,we get $a = \frac{10}{\sqrt{2}} = 5\sqrt{2} \, cm$.The area of a square is given by the formula $	ext{Area} = a^2$.Substituting the value of $a$,we get $	ext{Area} = (5\sqrt{2})^2 = 25 	imes 2 = 50 \, cm^2$.Alternatively,the area of a square can be calculated using the diagonal $d$ as $	ext{Area} = \frac{1}{2} 	imes d^2$.Substituting $d = 10 \, cm$,we get $	ext{Area} = \frac{1}{2} 	imes (10)^2 = \frac{1}{2} 	imes 100 = 50 \, cm^2$.

$PQRS$ is a square. If $PR = 10 \, cm$,then the area of $PQRS = \dots \, cm^2$.

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