Quadrilateral AreaDate: 04/29/2002 at 18:12:27 From: Aaron DeNOsaquo Subject: Area of Quadrilateral Given the (x,y) coordinates of four points, is there a simple formula to compute the area of the quadrilateral with corners on these 4 points? Date: 04/29/2002 at 18:29:39 From: Doctor Tom Subject: Re: Area of Quadrilateral Hi Aaron, Yes. If the points are (x1, y1), (x2, y2), ..., (x4, y4), then here's the formula: 2A = (x1y2 - x2y1) + (x2y3 - x3y2) + (x3y4 - x4y3) + (x4y1 - x1y4) (Notice the formula is for 2 times the area - to get the area, calculate the number on the right and divide by 2.) Also, the number you get will depend on whether you go clockwise or counter-clockwise around the quadrilateral. One direction will give the negative of the other, so to get the actual area, find the area as above and then take the absolute value. If the four points connecting 1 to 2 to 3 to 4 to 1 have lines that cross each other, the answer is meaningless - they have to form a simple region with an inside and an outside and no crossing lines. The formula does work for non-convex quadrilaterals, however. "Non-convex" means that there can be "indentations." Also, I hope that the pattern of the terms above is obvious. The same formula (but with more or fewer terms) will work for any simple polygon, from triangle on up. (A "simple" polygon is one whose edges do not cross each other.) - Doctor Tom, The Math Forum http://mathforum.org/dr.math/ Date: 04/29/2002 at 18:32:52 From: Aaron DeNOsaquo Subject: Area of Quadrilateral I just wanted to send thanks for the quick response. I am a grad student and am working on a finite element program. This will really help. Thanks again. |
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