Hostname: page-component-8448b6f56d-jr42d Total loading time: 0 Render date: 2024-04-18T19:48:55.843Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

Extract

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.

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Graumann, G., Investigating and ordering quadrilaterals and their analogies in space – problem fields with various aspects, ZDM 37 (3) (2005) pp. 190–198.Google Scholar
2. Josefsson, M., Properties of tilted kites, International Journal of Geometry 7 (1) (2018) pp. 87–104.Google Scholar
3. Coxeter, H. S. M. and Greitzer, S. L., Geometry revisited, Math. Ass. Amer. (1967).Google Scholar
4. Josefsson, M., Characterizations of trapezoids, Forum Geom. 13 (2013) pp. 23–35.Google Scholar
5. Josefsson, M., Properties of bisect-diagonal quadrilaterals, Math. Gaz. 101 (July 2017) pp. 214–226.10.1017/mag.2017.61Google Scholar
6. Josefsson, M., Properties of Pythagorean quadrilaterals, Math. Gaz. 100 (July 2016) pp. 213–224.10.1017/mag.2016.57Google Scholar
7. Josefsson, M., The area of a bicentric quadrilateral, Forum Geom. 11 (2011) pp. 155–164.Google Scholar
8. Josefsson, M., Metric relations in extangential quadrilaterals, International Journal of Geometry 6 (1) (2017) pp. 9–23.Google Scholar
9. Josefsson, M., On the classification of convex quadrilaterals, Math. Gaz. 100 (March 2016) pp. 68–85.10.1017/mag.2016.9Google Scholar
10. de Villiers, M., Some adventures in Euclidean geometry, Dynamic Mathematics Learning, 2009.Google Scholar
11. Josefsson, M., Properties of equidiagonal quadrilaterals, Forum Geom. 14 (2014) pp. 129–144.Google Scholar