How to find the sides of a polygon

In the broadest definition of a polygon, you can call any closed broken line. To calculate the lengths of the sides of such shapes based on a single formula is impossible. If you specify that the polygon is convex, then there will be some common to the entire class of shapes (e.g., the sum of the angles), but the total for all formulas of finding the side lengths of them won't be enough. If you narrow the definition even more and consider only regular convex polygons, it will be possible to deduce some common to all such figures of the calculation formulas of the parties.

Instruction

1. By definition, the right is called a polygon, the lengths of all sides which are identical. Therefore, knowing their total length is the perimeter (P) and the total number of vertices or sides (n), divide the former by the second to calculate the dimensions of each side (a) of the form: a = P/n.
2. About any correct polygon can be circumscribed by a circle is the only possible radius (R) is a property can also be used to calculate the length of side (a) of any polygon, if the number of vertices (n) is also known from the conditions. For this we consider the triangle formed by two radii and the desired side. This is an isosceles triangle in which the base can be found by multiplying twice the length of lateral side of radius - half the angle between them is the Central angle. Calculate the angle easily - divide 360° by the number of sides of the polygon. The final formula should look like this: a = 2*R*sin(180°/n).
3. A similar property is, and inscribed within a regular convex polygon of a circle - it is bound to exist, and the radius can have a single value for each particular shape. So here, when calculating the length of sides (a) you can use the knowledge of the radius (r) and the number of sides of polygon (n). The radius drawn from the point of tangency of the circle and any of the sides perpendicular to that side and divides it in half. Therefore, we consider a right triangle where the radius and half the required sides are the legs. According to the definition, their ratio is equal to the tangent of half the Central angle that you can calculate in the same way as in the previous step: (360°/n)/2 = 180°/n. Define tangent of an acute angle in a right triangle in this case can be written as: tg(180°/n) = (a/2)/r. Express from this equation the length of the side. You should get this formula: a = 2*r*tg(180°/n).