2. A regular polygon having five sides is known as
Answers
it is called pentagram. which have five sides
Answer:
A five-sided shape is called a pentagon. A six-sided shape is a hexagon, a seven-sided shape a heptagon, while an octagon has eight sides…
Step-by-step explanation:
All regular simple polygons (a simple polygon is one that does not intersect itself anywhere) are convex. Those having the same number of sides are also similar.
An n-sided convex regular polygon is denoted by its Schläfli symbol {n}. For n < 3, we have two degenerate cases:
Monogon {1}
Degenerate in ordinary space. (Most authorities do not regard the monogon as a true polygon, partly because of this, and also because the formulae below do not work, and its structure is not that of any abstract polygon.)
Digon {2}; a "double line segment"
Degenerate in ordinary space. (Some authorities do not regard the digon as a true polygon because of this.)
In certain contexts all the polygons considered will be regular. In such circumstances it is customary to drop the prefix regular. For instance, all the faces of uniform polyhedra must be regular and the faces will be described simply as triangle, square, pentagon, etc.
Angles Edit
For a regular convex n-gon, each interior angle has a measure of:
{\displaystyle \left(1-{\frac {2}{n}}\right)\times 180\,\,\,}{\displaystyle \left(1-{\frac {2}{n}}\right)\times 180\,\,\,} degrees, or equivalently {\displaystyle {\frac {180(n-2)}{n}}}{\displaystyle {\frac {180(n-2)}{n}}} degrees;
{\displaystyle {\frac {(n-2)\pi }{n}}}{\displaystyle {\frac {(n-2)\pi }{n}}} radians; or
{\displaystyle {\frac {(n-2)}{2n}}}{\displaystyle {\frac {(n-2)}{2n}}} full turns,
and each exterior angle (i.e., supplementary to the interior angle) has a measure of {\displaystyle {\tfrac {360}{n}}}{\tfrac {360}{n}} degrees, with the sum of the exterior angles equal to 360 degrees or 2π radians or one full turn.
As the number of sides, n approaches infinity, the internal angle approaches 180 degrees. For a regular polygon with 10,000 sides (a myriagon) the internal angle is 179.964°. As the number of sides increase, 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. For this reason, a circle is not a polygon with an infinite number of sides.
Diagonals Edit
For n > 2, the number of diagonals is {\displaystyle {\tfrac {1}{2}}n(n-3)}{\displaystyle {\tfrac {1}{2}}n(n-3)}; i.e., 0, 2, 5, 9, ..., for a triangle, square, pentagon, hexagon, ... . The diagonals divide the polygon into 1, 4, 11, 24, ... pieces OEIS: A007678.
For a regular n-gon inscribed in a unit-radius circle, the product of the distances from a given vertex to all other vertices (including adjacent vertices and vertices connected by a diagonal) equals n.
Points in the plane Edit
For a regular simple n-gon with circumradius R and distances di from an arbitrary point in the plane to the vertices, we have[1]
{\displaystyle {\frac {\sum _{i=1}^{n}d_{i}^{4}}{n}}+3R^{4}=\left({\frac {\sum _{i=1}^{n}d_{i}^{2}}{n}}+R^{2}\right)^{2}.}{\displaystyle {\frac {\sum _{i=1}^{n}d_{i}^{4}}{n}}+3R^{4}=\left({\frac {\sum _{i=1}^{n}d_{i}^{2}}{n}}+R^{2}\right)^{2}.}
Interior points Edit
For a regular n-gon, the sum of the perpendicular distances from any interior point to the n sides is n times the apothem[2]: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.[3][4]
Circumradius Edit