Areas Associated to a Quadrilateral

Oleg Mushkarov1), Nikolai Nikolov1,2)

1)Institute of Mathematics and Informatics, Bulgarian Academy of Sciences
2)University of Library Studies and Information Technologies

https://doi.org/10.53656/math2023-5-1-are

Abstract. We study the relationship between the areas of the consecutive quadrilaterals cut from a convex quadrilateral in the plane by means of a finite or infinite number of straight lines intersecting two of its opposite sides. Moreover, we obtain a geometric description of all possible areas obtained in this way given the ratios of the lengths of consecutive segments in which the lines divide these two opposite sides.
Keywords: quadrilateral; area; trihedral angle

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