Image a coordinate plane with points plotted at ordered pairs q(-4,4) r(2,4) s(5,-3) t(2,-3) and u (-4,-3) what is the area of the polygon qrstu

In counterclockwise order that's

R(2,4), Q(-4,4), U(-4,3), T(2,-3), S(5,-3)

That's a trapezoid, height 7 upper base 6, lower base 9, so average base 15/2 and area 7(15)/2 = 105/2 = 52.5.

52.5

The shoelace theorem gives the answer without thinking. We write the list on top of itself shifted and add up the cross produces:

R(2,4), Q(-4,4), U(-4,-3), T(2,-3), S(5,-3)

Q(-4,4), U(-4,-3), T(2,-3), S(5,-3), R(2,4),

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step-by-step explanation:

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