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jmc

geometry intermediate

Problem

When plotted in the standard rectangular coordinate system, trapezoid has vertices , , and . What is the area of trapezoid ?
Solution
The two bases of the trapezoids are the segments and , and the height is the perpendicular distance between the bases, which in this case is the difference of the -coordinates: . Similarly, the lengths of the bases are the differences of the -coordinates of their two endpoints. Using the formula , the area is square units.
Final answer
18