Suppose the polygon has vertices , , ... , , listed in clockwise order. Then area of is
The Shoelace Theorem gets its name because if one lists the the coordinates in a column, and marks the pairs of coordinates to be multiplied, the resulting image looks like laced-up shoes.
In right triangle , we have , , and . Medians and are drawn to sides and , respectively. and intersect at point . Find the area of .
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