The square is the right oneA quadrilateral or a rhombus, in which all sides are equal and form angles of 90 degrees between each other. The diagonal of the square is a segment that connects two opposite corners of the square. Find the diagonal of the square quite easily
So, it's worth starting with the fact that around the squareIt is possible to describe a circle whose diagonal is exactly equal to the diagonal of the square. In order to calculate the radius of the circumscribed circle, it is necessary to use the formula:
R = (v2 * a) / 2, where a is the side of the square.
Also in the box you can enter a circle. The circle at the points of contact with the sides of the square divides them in half. The formula with which you can calculate the radius of the inscribed circle looks like this:
R = a / 2
If, in solving the problem, the radius is knownCircle that is inscribed in a given square, then it is possible in this way to express also the side of the square, the value of which is necessary for finding the diagonal of the square:
A = 2 * r
The length of the radius of the circle is equal to half the length of its diagonal. Thus, the length of the diagonal of the circumscribed circle, and, hence, the length of the diagonal of the square can be calculated by the formula:
D = v2 * a
For greater clarity, you can consider a small example:
Given a square with a side length of 9 cm, it is required to find the length of its diagonal.
Solution: in order to calculate its length, you will need to use the formula above:
D = v2 * 9
D = v162 cm
Answer: the length of the diagonal of a square with a side of 9 cm is v162 cm or, approximately, 14.73 cm