A square is a quadrilateral, possessing four sides all equal in length and four right angles. The shape has some degree of symmetry; the diagonals are of equal length and bisect each other at right angles.

Diagonal Of Square

The diagonal of a square is said to be the line which connects the opposite corners of a square. It splits the square into two equal halves of triangle.

If you work with a formula, the length of the diagonal may come very easily. Take a length of one of the square's sides and multiply it by the square root of two. This is based on the geometric relation derived from the Pythagorean theorem, which refers to the right triangles that are formed by drawing the diagonal.

Length of the Diagonal 

Draw a square ABCD whose sides are equal to 'a' cm.

Draw two diagonals AD and BC from the square ABCD.

 

From the diagram it can be seen that, the diagonal divides the square into two right triangle, i,e,

Taking any one of the above triangles to determine the length of the diagonal.

In,

ΔACD

 , we apply Pythagoras Theorem to find the diagonal.

................(i)

we know AC = CD = a, …………………….(ii)

Now substituting the value of (ii) in (i), we have

Thus the length of the diagonal of the given square is,

Solved Problem

Problem 1- Find the length of a diagonal of a square whose side is 4 cm.

Solution- Given a = 4 cm

Length of a diagonal =

Problem 2: Find the length of a diagonal of a square, given its area to be 64

Solution- Given Area = 64

We know, Area =

Now Length of a diagonal =

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