Area and perimeter relationship for different shapes with an inradius
Keywords:
geometry, measurementAbstract
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
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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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Copyright (c) 2022 Richard Kaufman
