What is the Formula for Perimeter of a Square?
Square is a rectangle whose adjacent sides are equal in length. This means it is a quadrilateral where all the sides are equal in length. Each of the angles in a square is a right angle.
- All four sides of a square are equal in length
- The diagonals of a square are equal
- The diagonals of a square bisect each other at right angles
- All the four angles of a square are right angles
Perimeter of a Square
Perimeter refers to the sum of all the sides of a polygon. For a square, it will be the sum of its four equal sides, i.e. four times the length of a side.
Let’s consider a square with each side of length equal to ‘a’ units.
Perimeter = Sum of all sides of square = a + a + a + a = 4a units
Thus, the perimeter of a square with the length of each side equal to ‘a’ units is given by 4a.
Question 1: Find the perimeter of a square each of side 5 cm.
Length of each side of the square = 5 cm
Perimeter of the square = sum of all sides = 5 + 5 + 5 + 5 = 20 cm
Thus, perimeter of square = 20 cm
Question 2: Find the length of sides of a square with a perimeter of 48 cm.
Given perimeter of the square = 48 cm
Lets length of each side of the square = ‘a’ cm
Therefore, perimeter = 4a cm
Therefore, we can write:
4a = 48 cm
a = 12 cm
Thus, length of each side of square is 12 cm.
Question 3: Find the perimeter of a square whose length of diagonal is 4√2 cm.
Given, the length of a diagonal square = 4√2 cm.
Let the length of each side of the square = a cm.
Thus, applying the Pythagoras theorem, the length of diagonal = √(a2+a2) = a√2 cm
So, we can write:
a√2 = 4√2
a = 4 cm
Thus, the perimeter of square = 4a = 4 × 4 = 16 cm
Question 4: Find the sum of adjacent sides of a square given perimeter of the square is 12 cm.
Given the perimeter of the square = 12 cm
Considering length of each side = ‘a’ cm, the perimeter = 4a cm
Thus, we can write:
4a = 12
a = 3 cm
Since adjacent sides of a square are having the same length, we can write the sum of any adjacent sides of the square = a + a = 2a
Therefore, the sum of adjacent sides of the square = 2 × 3 = 6 cm