Difference between revisions of "Shoelace Theorem"

Revision as of 13:07, 24 April 2008

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

Let the coordinates, in "clockwise" order, be $(a_1, b_1)$ , $(a_2, b_2)$ , ... , $(a_n, b_n)$ . The area of the polygon is

$\dfrac{1}{2} |a_1b_2+a_2b_3+\cdots +a_nb_1-b_1a_2-b_2a_3-\cdots -b_na_1|.$

Shoelace Theorem gets it's name by listing the coordinates like so:

$(a_1, b_1)$ $(a_2, b_2)$ $\vdots$ $(a_n, b_n)$ $(a_1, b_1)$

This article is a stub. Help us out by expanding it.

Revision as of 13:05, 24 April 2008 (view source) 1=2 (talk \| contribs) ← Older edit		Revision as of 13:07, 24 April 2008 (view source) 1=2 (talk \| contribs) Newer edit →
Line 20:		Line 20:

	[[Category:Geometry]]		[[Category:Geometry]]
−	[[Category:~~Theorem~~]]	+	[[Category:Theorems]]