Search results
Results From The WOW.Com Content Network
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
All vertices of a regular polygon lie on a common circle (the circumscribed circle); i.e., they are concyclic points. That is, a regular polygon is a cyclic polygon . Together with the property of equal-length sides, this implies that every regular polygon also has an inscribed circle or incircle that is tangent to every side at the midpoint.
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 ...
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 .
Contracting an edge of a polygon-circle graph results in another polygon-circle graph. A geometric representation of the new graph may be formed by replacing the polygons corresponding to the two endpoints of the contracted edge by their convex hull. Alternatively, in the alternating sequence representing the original graph, combining the ...
The common length of the sides equals the radius of the circumscribed circle or circumcircle, which equals times the apothem (radius of the inscribed circle). All internal angles are 120 degrees . A regular hexagon has six rotational symmetries ( rotational symmetry of order six ) and six reflection symmetries ( six lines of symmetry ), making ...
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 the vertices of the pentagon. The fifth vertex is the rightmost intersection of the horizontal line with the original circle.
The regular finite polygons in 3 dimensions are exactly the blends of the planar polygons (dimension 2) with the digon (dimension 1). They have vertices corresponding to a prism ({n/m}#{} where n is odd) or an antiprism ({n/m}#{} where n is even). All polygons in 3 space have an even number of vertices and edges.