Shoelace Theorem
The Shoelace Theorem is a nifty formula for finding the area of a polygon given the coordinates of it's vertices.
Theorem
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.
Proof
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