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Apothem of a hexagon Graphs of side, s; apothem, a; and area, A of regular polygons of n sides and circumradius 1, with the base, b of a rectangle with the same area. The green line shows the case n = 6. The apothem (sometimes abbreviated as apo [1]) of a regular polygon is a line
The apothem is half the cotangent of /, and the area of each of the 14 small triangles is one-fourth of the apothem. The area of a regular heptagon inscribed in a circle of radius R is 7 R 2 2 sin 2 π 7 , {\displaystyle {\tfrac {7R^{2}}{2}}\sin {\tfrac {2\pi }{7}},} while the area of the circle itself is π R 2 ; {\displaystyle \pi R^{2 ...
Regular convex and star polygons with 3 to 12 vertices labelled with their Schläfli symbols. These properties apply to all regular polygons, whether convex or star: A regular n-sided polygon has rotational symmetry of order n. All vertices of a regular polygon lie on a common circle (the circumscribed circle); i.e
These segments are called its edges or sides, and the points where two of the edges meet are the polygon's vertices (singular: vertex) or corners. The word polygon comes from Late Latin polygōnum (a noun), from Greek πολύγωνον ( polygōnon/polugōnon ), noun use of neuter of πολύγωνος ( polygōnos/polugōnos , the masculine ...
The area of a regular polygon is given in terms of the radius r of its inscribed circle and its perimeter p by A = 1 2 ⋅ p ⋅ r . {\displaystyle A={\tfrac {1}{2}}\cdot p\cdot r.} This radius is also termed its apothem and is often represented as a .
Mark its intersection with the horizontal line (inside the original circle) as the point W and its intersection outside the circle as the point V. Draw a circle of radius OA and center W. It intersects the original circle at two of the vertices of the pentagon. Draw a circle of radius OA and center V. It intersects the original circle at two of ...
In geometry, a 65537-gon is a polygon with 65,537 (2 16 + 1) sides. The sum of the interior angles of any non– self-intersecting 65537-gon is 11796300°. Regular 65537-gon
In geometry, a curve of constant width is a simple closed curve in the plane whose width (the distance between parallel supporting lines) is the same in all directions. The shape bounded by a curve of constant width is a body of constant width or an orbiform, the name given to these shapes by Leonhard Euler. [1]