If (1, 1),(3, 4),(5, -2),and (4, -7) are the | vedclass

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(B) The area of a quadrilateral with vertices $(x_1, y_1)$,$(x_2, y_2)$,$(x_3, y_3)$,and $(x_4, y_4)$ is given by the formula: $	ext{Area} = \frac{1}

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$20.5$

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(B) The area of a quadrilateral with vertices $(x_1, y_1)$,$(x_2, y_2)$,$(x_3, y_3)$,and $(x_4, y_4)$ is given by the formula: $	ext{Area} = \frac{1}{2} |(x_1y_2 + x_2y_3 + x_3y_4 + x_4y_1) - (y_1x_2 + y_2x_3 + y_3x_4 + y_4x_1)|$. Substituting the given coordinates $(1, 1)$,$(3, 4)$,$(5, -2)$,and $(4, -7)$: $	ext{Area} = \frac{1}{2} |(1 	imes 4 + 3 	imes -2 + 5 	imes -7 + 4 	imes 1) - (1 	imes 3 + 4 	imes 5 + -2 	imes 4 + -7 	imes 1)|$. $	ext{Area} = \frac{1}{2} |(4 - 6 - 35 + 4) - (3 + 20 - 8 - 7)|$. $	ext{Area} = \frac{1}{2} |(-33) - (8)|$. $	ext{Area} = \frac{1}{2} |-41| = 20.5 	ext{ square units}$.

If $(1, 1)$,$(3, 4)$,$(5, -2)$,and $(4, -7)$ are the vertices of a quadrilateral,find its area.

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