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).