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Area formulas for certain convex quadrilaterals

Published online by Cambridge University Press:  14 February 2019

Martin Josefsson
Martin Josefsson*
Affiliation:
Västergatan 25d, 285 37 Markaryd, Sweden e-mail: martin.markaryd@hotmail.com

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The purpose of this paper is to collect for the first time area formulas for all convex quadrilaterals that can be expressed in terms of their four sides alone. There are presently 23 such classes that we know of. Many mathematics teachers would probably find it challenging just to name that many different classes of quadrilaterals, and even more difficult to tell how to calculate their different areas. Several of these classes of quadrilaterals are included neither in MathWorld, Wikipedia nor in any other encyclopedia that we know of. The formulas can be sorted into four categories as either well known, a special case of another formula, less known, or previously unknown (at least to us). The last category only includes two formulas and we will prove these.

Information

Type
Articles
Information
The Mathematical Gazette , Volume 103 , Issue 556 , March 2019, pp. 20 - 27
Copyright
Copyright © Mathematical Association 2019 

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