The square represents the correct quadrangle or a rhombus at which all parties are equal and form among themselves corners in 90 degrees. Square diagonal - a piece which connects among themselves two opposite corners of a square. To find square diagonal rather easily
Instruction
1. So, it is worth beginning with the fact that around a square it is possible to describe a circle which diagonal is equal in accuracy to square diagonal. To count the radius of a circumscribed circle, it is necessary to use a formula: R = (√2*a)/2 where an is the party of a square. Also it is possible and to enter a circle in a square. At the same time the circle in points of contact it with the parties of a square halves them. The formula by means of which it is possible to calculate the radius of an inscribed circle looks so: r = a/2esli, at the solution of a task, the circle radius which is entered in this square is known, it is possible to express thus and the party of a square which size is necessary for finding of diagonal of a square: a = 2*r
2. Length of radius of a circle is equal to a half of length of its diagonal. Thus, length of diagonal of a circumscribed circle, and, so and length of diagonal of a square can be calculated by a formula: d = √2*a
3. For bigger clarity, it is possible to review a small example: The square with a length of party of 9 cm is given, it is required to find length of its diagonal. Decision: to count its length, it will be required to use a formula above: d = √2*9d = √162 smotvt: square diagonal length with the party of 9 cm is equal √162 cm or, about, 14.73 cm