# How to find the diagonal of the quadrilateral

Quadrangle called the figure of four sides and corners, adjacent to them. Among these pieces are rectangular, trapezoid, parallelogram. In a number of tasks required to find the geometry of the diagonal of one of these shapes.

## Instruction how to find the diagonal of the quadrilateral

Step 1:

Diagonal of the quadrangle called the segment connecting its opposite corners. In quadrilateral has two diagonals which intersect each other at one point. Diagonals are sometimes equal, as in a rectangle and a square, and sometimes have different lengths, as, for example, a trapezoid. diagonal method depends on finding figury.Postroyte rectangle with sides a and b and the two diagonals d1 and d2. From the known properties of the rectangle that its diagonals are equal to each other, they intersect at one point and divide it in half. If you know the two sides of the rectangle, then its diagonals are found as follows: d1 = √a ^ 2 + b ^ 2 = d2.Chastnym case of a rectangle is a square, whose diagonal is a√2. In addition, the diagonal can be found, knowing the area of the square. It is equal to: S = d ^ 2 / 2.Otsyuda diagonal length calculated by the formula: d = √2S.

Step 2:

Several otherwise solve the problem, when not given a rectangle, and a parallelogram. In this figure, in contrast to the rectangular or square, are equal, not all the angles, but only the opposite. If the condition is present task parallelogram with sides a and b and a predetermined angle between them, as shown in step, then get the diagonal, using the cosine theorem: d ^ 2 = a ^ 2 + b ^ 2-2ab * cosα.Parallelogramm, having equal sides is called a rhombus. If the terms of the problem it is necessary to find a diagonal of this figure, the required value of its second diagonal and square, as the diagonal of the figure equal. Formula rhombus area as follows: S = d1 * d2 / 2.Otsyuda d2 is twice the square figure divided by d1: d2 = 2S / d1.

Step 3:

When calculating the area of a trapezoid have to use the trigonometric function sine. If this figure is equilateral, then, knowing her first diagonal d1 and the angle between the two diagonals AOD, as shown by step, get the second by the following formula: d2 = 2S / d1 * sinφ. In this case, we consider a trapezoid ABCD.Suschestvuet also rectangular trapezoid, the diagonal of which is somewhat easier to find. Knowing the length of the side of the trapezoid, which coincides with its height, and the lower base, find the diagonal, using the usual Pythagorean theorem. Namely fold the squares of these values, and then remove from the result of the square root.