The simplest formula for calculating the area of ​​ square (S) would be the case if you know the length of the part (a) of the figure - just multiply it to itself (squared): S = a².
If the conditions of the problem given the length of the perimeter (P) of this figure to the above formula, it is necessary to add another mathematical operation.Since the perimeter of the sum of the lengths of all sides of a polygon, a square, it contains four equal terms, i.e.length of each side can be written as P / 4.Put this value in the previous step.You should have such
an equation: S = P² / 4² = P² / 16.
Diagonal square (L) connects two of its opposite vertices to form together with the two sides of a right triangle.This feature allows you to pieces using the Pythagorean theorem (L² = a² + a²) along the length of the diagonal length of the side compute (a = L / √2).Substitute this expression, and all the same formula from the first step.In general, the solution should look like this: S = (L / √2) ² = L² / 2.
can calculate the area of ​​a square and diameter (D) described a circle around him.Since the diagonal of any regular polygon coincides with the diameter of the circle, in the formula of the previous step replace only the designation of a diagonal diameter designation: S = D² / 2.If you want to express area not in diameter, and in a radius (R), convert the equity in such a way: S = (2 * R) ² / 2 = 2 * R².
Calculating area of ​​diameter (d) of the inscribed circle a little more difficult, as in relation to the square of this value is always equal to the length of its side.As in the previous step for the calculation formula you only need to replace the designation already described above equality - this time engage the identity of the first step: S = d².If necessary, use instead diameter radius (r), transform this formula as: S = (2 * r) ² = r² * 4.