In geometry, a square is a regular quadrilateral that has four equal sides and four angles which are
Diagonal of a square-
A square can have two diagonals. Each of the diagonal can be formed by joining the diagonally opposite vertices of a square. The properties of diagonals are as follows-
- Both the diagonals are congruent (same length).
- Both the diagonals bisect each other, i.e. the point of joining of the two diagonals is the midpoint of both the diagonals.
- A diagonal divides a square into two isosceles right-angled triangles.
Length of the Diagonal-
Consider a square ABCD having sides equal to ‘a’ cm.
Let AD and BC be the two diagonals of a square.
It is clearly visible that a diagonal divides the square into two right triangle, i,e,
Let us take any triangle of the two for calculating the length of the diagonal.
we know AC = CD = a, …………………….(ii)
Substituting the value of (ii) in (i), we have
Thus the length of the diagonal of the given square is-
Example 1- Find the length of a diagonal of a square whose side is 4 cm.
Solution- Given a = 4 cm
Length of a diagonal =
Example 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 =