The perimeter characterizes length of the closed contour. As well as the area, it can be found in other sizes specified in a statement of the problem. Tasks on finding of perimeter very often meet in a school course of mathematics.
Instruction
1. Knowing perimeter and the party of a figure, it is possible to find other its party and also the area. The perimeter, in turn, can be found on several set parties or on a corner and the parties, depending on statements of the problem. Also in some cases it is expressed through the area. Most just there is a rectangle perimeter. Draw a rectangle from one of the parties equal and, and the diagonal equal to d. Knowing these two sizes, find other its party which is rectangle width on Pythagorean theorem. Having found rectangle width, calculate its perimeter as follows: p=2(a+b). This formula is fair for all rectangles as at any of them four parties.
2. Pay attention to that fact that the triangle perimeter in the majority of tasks is found in the presence of information at least on one its coal. However, there are also tasks in which all parties a triangle are known, and then the perimeter can be calculated by simple summation, without use of trigonometrical calculations: p=a+b+c, where a, b and c - the parties. But such tasks occur in textbooks seldom as the way of their decision is obvious. Solve more complex problems of finding of perimeter of a triangle step by step. For example, draw an isosceles triangle at which the basis and a corner are known at it. To find its perimeter, in the beginning find the parties of an and b as follows: b=c/2cosα. As a=b (a triangle isosceles), draw the following conclusion: a=b=c/2cosα.
3. Calculate perimeter of a polygon the same way, putting lengths of all its parties: p=a+b+c+d+e+f and so on. If the regular polygon is also inscribed in a circle or described about it, calculate length of one of its parties, and then increase by their quantity. For example, to find the parties of a hexagon, inscribed in a circle, act as follows: a=R where an is the party of a hexagon equal to the radius of a circumscribed circle. Respectively, if the hexagon the correct, then its perimeter is equal: p=6a=6R. If the circle is entered in a hexagon, then the party of the last is equal: a=2r√3/3. Respectively, find perimeter of such figure as follows: p=12r√3/3.