Perimeter call the total length of all parties of a geometrical figure. Usually it is found method of addition of the sizes of the parties. With a regular polygon the perimeter can be found in a case, having increased piece length between tops by quantity of such pieces. The square belongs to such type of polygons. Knowing its perimeter, it is possible to find length of its party by means of only one arithmetic action.
It is required to you
- - calculator.
Instruction
1. Consider any square. Remember its properties. It has 4 parties, and all of them are identical on length and are located on the relation to each other at right angle. Designate the party of a square as and, and perimeter — as river.
2. Remember how to find the size of a part of any object if these parts are equal, and the quantity them is known to you. It can be done, having divided whole into quantity of parts. Present perimeter as the whole object, then each party will be its part. In total these Parts four. That is the size of the party can be found, having divided perimeter into 4. It is possible to express it formula a=p/4.
3. In precisely the same way, knowing perimeter, it is possible to find the size of the party of any regular polygon. For a pentagon the formula and = r/5, for a hexagon — and = r/6 , etc. is fair.
4. Think at what else polygon 4 parties, and thus they are equal among themselves. It is a rhombus which special case many mathematicians consider a square. At a rhombus the corners belonging to one party are not equal among themselves, but for calculation of perimeter it does not play any role. The party of any rhombus can be found just as the party of a square, that is having divided perimeter into 4.
5. Knowing square perimeter, it is possible to find some more sizes important for this geometrical figure. Make additional construction, having entered a circle in a square. Carry out diameter so that it connected points of contact of a circle to the opposite parties of a square. Diameter is equal to the party of this geometrical figure. And it means, as it can be found precisely in the same way, that is having divided perimeter into 4. It is possible to express it formula d=p/4.
6. In tasks not the diameter of a circle, but its radius very often is required. It is possible to find it, having divided diameter into 2. And if to try to express radius through perimeter, the formula r=d/2= will turn out (p: 4)/2= r/8.
7. Through perimeter it is possible to express also the radius of a circumscribed circle. Construct it and carry out the radius which will cross a circle in one of square tops. From the center of a circle carry out a perpendicular to one of the parties of this corner. At you the rectangular triangle at which besides legs are equal turned out, and one also is the radius of an inscribed circle, that is its size is equal r/8. Radius of a circumscribed circle represents a hypotenuse of this triangle, and it is possible to find it on Pythagorean theorem, that is R^2=(p/8) ^2+(p/8) ^2=2(p/8) ^2.