The figure formed more than from two lines which are becoming isolated among themselves is called a polygon. Each polygon has tops and the parties. Any of them can be correct or wrong.
Instruction
1. A regular polygon is called the figure at which all parties are equal. So, for example, the equilateral triangle represents the regular polygon consisting of three closed lines. In this case, all its corners are equal 60 °. Its parties are among themselves equal, but are not parallel each other. The same property also others polygons have, however, corners at them have other sizes. Only of regular polygons at which the parties not only are equal but also are in pairs parallel - a square. If in a task the equilateral triangle with an area of S is given, then its unknown party can be found through corners and the parties. First of all, find h triangle height perpendicular to its basis: h=a*sinα=a√3/2, where α=60 ° - one of the corners adjacent to the triangle basis. Being guided by these reasons, transform a formula for finding of the area so that on it it was possible to calculate length of the party: S=1/2a*a√3/2=a^2 * √ 3/4otsyuda follows that the party of an is equal: a=2√S / √√ 3
2. Find the party of the correct quadrangle, using a bit different way. If it represents a square, as initial data use its area or diagonal: S=a^2Следовательно, the party of an is equal: a= √ SKrome of if diagonal is given, then the party can be calculated also on other formula: a=d / √ 2
3. In most cases the party of a regular polygon can be defined, knowing the radius of the circle entered in it or described around it. It is known that there is an interrelation between the party of a triangle and radius of the circle described around this figure: a3=R√3 where R - the radius of the described okruzhnostiyesla a circle is inscribed in a triangle, a formula takes other form: a3=2r√3 where r is the radius of the party entered to an okruzhnosti of the correct hexagon a formula for location at the known radius of described (R) or entered (r) of circles looks as follows: a6=R=2r3/3iz of these examples can draw a conclusion that for any any n-square the formula for finding of the party in a general view looks as follows: a=2Rsin(α/2) =2rtg(α/2)