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The area of a regular decagon of side length a is given by: [3] = = + In terms of the apothem r (see also inscribed figure), the area is: = = In terms of the circumradius R, the area is:
The area of a regular dodecagon of side length a is given by: = = (+) And in terms of the apothem r (see also inscribed figure), the area is: = = In terms of the circumradius R, the area is: [1]
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
For a regular n-gon, the sum of the perpendicular distances from any interior point to the n sides is n times the apothem [4]: p. 72 (the apothem being the distance from the center to any side). This is a generalization of Viviani's theorem for the n = 3 case. [5] [6]
A circular segment (in green) is enclosed between a secant/chord (the dashed line) and the arc whose endpoints equal the chord's (the arc shown above the green area). In geometry , a circular segment or disk segment (symbol: ⌓ ) is a region of a disk [ 1 ] which is "cut off" from the rest of the disk by a straight line.
The surface area and the volume of a ... is the apothem of a regular pentagon ... one pentagon connected to odd vertices of the decagon and the other pentagon ...
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A regular icositrigon has internal angles of degrees, with an area of = = , where is side length and is the inradius, or apothem. The regular icositrigon is not constructible with a compass and straightedge or angle trisection , [ 1 ] on account of the number 23 being neither a Fermat nor Pierpont prime .