Difference between revisions of "Shoelace Theorem"
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== Problems == | == Problems == | ||
=== Introductory === | === Introductory === | ||
− | In right triangle <math>ABC</math>, we have <math>\angle ACB=90^{\circ}</math>, <math>AC=2</math>, and <math>BC=3</math>. [[ | + | In right triangle <math>ABC</math>, we have <math>\angle ACB=90^{\circ}</math>, <math>AC=2</math>, and <math>BC=3</math>. [[Median]]s <math>AD</math> and <math>BE</math> are drawn to sides <math>BC</math> and <math>AC</math>, respectively. <math>AD</math> and <math>BE</math> intersect at point <math>F</math>. Find the area of <math>\triangle ABF</math>. |
Revision as of 10:47, 3 May 2009
The Shoelace Theorem is a nifty formula for finding the area of a polygon given the coordinates of its vertices.
Contents
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
Problems
Introductory
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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