P(2, 1), Q(4, -1), R(3, 2) are the vertices o | vedclass

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(B) The quadrilateral $PQRS$ formed by drawing lines through the vertices parallel to the opposite sides is a parallelogram.The area of this parallelo

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$4$

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(B) The quadrilateral $PQRS$ formed by drawing lines through the vertices parallel to the opposite sides is a parallelogram.The area of this parallelogram $PQRS$ is twice the area of the triangle $\Delta PQR$.The area of $\Delta PQR$ with vertices $(x_1, y_1), (x_2, y_2), (x_3, y_3)$ is given by:$	ext{Area} = \frac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|$Substituting the coordinates $P(2, 1), Q(4, -1), R(3, 2)$:$	ext{Area}(\Delta PQR) = \frac{1}{2} |2(-1 - 2) + 4(2 - 1) + 3(1 - (-1))|$$= \frac{1}{2} |2(-3) + 4(1) + 3(2)|$$= \frac{1}{2} |-6 + 4 + 6| = \frac{1}{2} |4| = 2$Therefore,the area of the parallelogram $PQRS = 2 	imes 	ext{Area}(\Delta PQR) = 2 	imes 2 = 4$.

$P(2, 1), Q(4, -1), R(3, 2)$ are the vertices of a triangle. If lines parallel to the opposite sides are drawn through $P$ and $R$ to intersect at $S$,then the area of $PQRS$ is:

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