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A perimeter is a closed path that encompasses, surrounds, or outlines either a two dimensional shape or a one-dimensional length. The perimeter of a circle or an ellipse is called its circumference. Calculating the perimeter has several practical applications. A calculated perimeter is the length of fence required to surround a yard or garden.
The constant width of these shapes allows their use as coins that can be used in coin-operated machines. For instance, the United Kingdom has made 20-pence and 50-pence coins in the shape of a regular Reuleaux heptagon. [5] The Canadian loonie dollar coin uses another regular Reuleaux polygon with 11 sides. [6]
The apothem a can be used to find the area of any regular n-sided polygon of side length s according to the following formula, which also states that the area is equal to the apothem multiplied by half the perimeter since ns = p.
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 .
The Reuleaux triangle can be generalized to regular or irregular polygons with an odd number of sides, yielding a Reuleaux polygon, a curve of constant width formed from circular arcs of constant radius. The constant width of these shapes allows their use as coins that can be used in coin-operated machines. [9]
As the number of sides increases, the internal angle can come very close to 180°, and the shape of the polygon approaches that of a circle. However the polygon can never become a circle. The value of the internal angle can never become exactly equal to 180°, as the circumference would effectively become a straight line (see apeirogon). For ...