From: kovarik@mcmail.cis.McMaster.CA (Zdislav V. Kovarik) Subject: Re: Area Calculation Date: 3 Feb 1999 19:28:09 -0500 Newsgroups: sci.math Keywords: Area of a quadrilateral In article , golfer wrote: :Thanks in advance to all who read this and help me out...... : :Issue: : : I have an area of land that is reserved by the county and I am : trying to build on it. The County may allow me to reallocate : another portion of my land in lieu of the existing reserved area. : :Problems; : : 1) I have a quadrilateral area with sides in length of; : a) 67.5 feet : b) 102.5 feet : c) 125 feet : d) 150 feet : : What is the total area? As others have remarked, the shape and area is not well defined; you need one diagonal. It is possible to obtain the maximal possible area of a quadrilateral with given lengths of sides (I presume they are listed in cyclic order). The shape must be such that the quadrilateral can be inscribed in a circle. The optimal length of the diagonal separating sides a, b from sides c, d is the square root of ((a^2 + b^2) * c * d + (c^2 + d*2) * a * b) / (a * b + c * d) and in your case, it is about 145.8724 units. The maximal possible area is about 11466.418 square units. The angle between c and d is about 63.3055 degrees. If the angle between your c and d is not as the one above, your area will be smaller than the maximal one, given the same lengths of sides as traced cyclically. Still, as remarked elsewhere, the (x,y) coordinates of the corner points in any rectangular coordinate system are enough to calculate the actual area using a form of Green's formula. Cheers, ZVK(Slavek).