Find the area of the pentagon with vertices A | vedclass

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(C) The area of a polygon with vertices $(x_1, y_1), (x_2, y_2), \dots, (x_n, y_n)$ is given by the formula: $	ext{Area} = \frac{1}{2} |(x_1y_2 - y_1

Vedclass · Accepted Answer

$137/2$

Vedclass · Answer

(C) The area of a polygon with vertices $(x_1, y_1), (x_2, y_2), \dots, (x_n, y_n)$ is given by the formula: $	ext{Area} = \frac{1}{2} |(x_1y_2 - y_1x_2) + (x_2y_3 - y_2x_3) + (x_3y_4 - y_3x_4) + (x_4y_5 - y_4x_5) + (x_5y_1 - y_5x_1)|$. \ Substituting the given points $A(1, 1), B(7, 21), C(7, -3), D(12, 2), E(0, -3)$: \ $	ext{Area} = \frac{1}{2} |(1 	imes 21 - 1 	imes 7) + (7 	imes -3 - 21 	imes 7) + (7 	imes 2 - (-3) 	imes 12) + (12 	imes -3 - 2 	imes 0) + (0 	imes 1 - (-3) 	imes 1)|$ \ $	ext{Area} = \frac{1}{2} |(21 - 7) + (-21 - 147) + (14 + 36) + (-36 - 0) + (0 + 3)|$ \ $	ext{Area} = \frac{1}{2} |14 - 168 + 50 - 36 + 3| = \frac{1}{2} |-137| = \frac{137}{2} 	ext{ square units}$.

Find the area of the pentagon with vertices $A(1, 1)$,$B(7, 21)$,$C(7, -3)$,$D(12, 2)$,and $E(0, -3)$.

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