The polygon consists of several pieces connected among themselves and forming the closed line. All figures of this class are divided into simple and difficult. The triangle and a quadrangle, and to difficult - polygons with a large number of the parties and also star-shaped polygons belong to simple.
Instruction
1. Most often in tasks the correct triangle meets the party of a. As the polygon is regular, all three of its parties are equal. Therefore, knowing a median and height of a triangle, it is possible to find all its parties. For this purpose use method of finding of the party through a sine: a=x/cosα.Так as the party of a triangle are equal, i.e. a=b=c=a, a=b=c=x/cosα where x - height, a median or a bisector. The same way you find all three unknown parties in an isosceles triangle, but under one condition - assigned altitude. It has to be projected on the triangle basis. Knowing height of the basis x, find the party of an isosceles triangle of a: a=x/cosα.Поскольку a=b as a triangle isosceles, find its parties as follows: as you found a=b=x/cosα.После of that triangle sides, calculate triangle basis length, applying Pythagorean theorem to finding of a half of the basis: with / 2= √ ()^2-(x^2)= √ x^2 (1-cos^2α)/cos^2α=xtgα.Отсюда find x/cosα the basis: c=2xtgα.
2. The square represents the correct quadrangle which parties are calculated in several ways. Below each of them is considered. The first way offers finding of the party through square diagonal. As all corners at a square straight lines, this diagonal halves them in such a way that two rectangular triangles with corners of 45 degrees at the basis are formed. Respectively, the party of a square is equal: a=b=c=f=d*cosα=d√2/2 where d is square diagonal. If the square is inscribed in a circle, then knowing the radius of this circle, find its party: a4=R√2 where R is circle radius.
3. At multilateral polygons calculate the party the last of the offered ways - by description of a polygon in a circle. For this purpose draw a regular polygon with any parties, and around it describe a circle with the set R.Predstavte radius to yourself that in a task some any n-square is given. If the circle is described about this polygon, then apply a formula to finding of the party: an=2Rsinα/2.