Area and perimeter relationship for different shapes with an inradius

Authors

  • Richard Kaufman UMass Lowell

Keywords:

geometry, measurement

Abstract

In this paper, we show that an interesting relationship for a triangle, which is Area/Perimeter = r/2, extends to other shapes with an inradius r (i.e., shapes with an inscribed circle). These shapes include squares, circles, rhombuses, regular polygons, and even irregular polygons and more.

References

Incircle and excircles of a triangle. (July 10, 2022). In Wikipedia. https://en.wikipedia.org/wiki/Incircle_and_excircles_of_a_triangle#cite_note-9

Area of Triangle in Terms of Inradius. (July 10, 2022). In ProofWiki. https://proofwiki.org/wiki/Area_of_Triangle_in_Terms_of_Inradius

Chu, T. (2005). Problem 584. The Pentagon, 65(1), 50. Available online at https://www.kappamuepsilon.org/Pentagon/Vol_65_Num_1_Fall_2005.pdf

Ogilvy, C. S., & Anderson, J. T. (1988). Excursions in number theory. Dover Publications, 68.

Rhombus. (July 10, 2022). In Wikipedia. http://en.wikipedia.org/w/index.php?title=Rhombus&oldid=650988704

Apothem. (July 10, 2022). In Wikipedia. http://en.wikipedia.org/w/index.php?title=Apothem&oldid=650696918

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Published

2022-09-24

How to Cite

Kaufman, R. (2022). Area and perimeter relationship for different shapes with an inradius. Ohio Journal of School Mathematics, 92(1), 27–31. Retrieved from https://ohiomathjournal.org/index.php/OJSM/article/view/9155

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Articles

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