Perimeter of a Square: formula & Solved questions

The perimeter of a square is the total distance at the boundaries or outside the square. The perimeter of any closed figure is calculated by finding the sum of all the sides. A Square is a quadrilateral with four equal sides, thus, the sum of the length of all four sides will be the perimeter of a square. Since all of its sides are equal, the perimeter is taken to be four times the length of one side.

In other words, the perimeter is the distance around a closed figure. It is the length of a shape or path that encompasses it. Therefore, the closed figure, being a square, its perimeter will be;

P = 4 × side

Or P = 4a, where a will be the side of square

Key terms: Perimeter, Square, Sum of lengths, Properties of square, perimeter Formula, Diagonals

---

What is a square?

[Click Here for Sample Questions]

Square is a rectangular quadrilateral with four equal sides and equal angles, with each angle being 90°. It is a plane figure with four equal and parallel sides. It can even be referred to as a rectangle, with the two adjacent sides being equal. If the vertices of a square are A, B, C, and D, then the figure would be denoted as ABCD. 

Square

Also read: Types of polygon

---

Properties of a square

[Click Here for Sample Questions]

A square is a 4-sided closed figure. The properties of a square are used in many applications. The following mentioned are some important properties of a square.

• The diagonals of a square bisect each other.
• The diagonals of a square are perpendicular to each other.
• All four sides of a square are of equal length.
• Opposite sides of a square are both equal and parallel.
• All the four angles of a square are equal and right-angled. (Square is 360°/4 = 90 degrees)
• The diagonals of a square are equal in length.

Also read: Area of square

---

Perimeter of square formula

[Click Here for Sample Questions]

Since, the perimeter is the distance around a closed figure, the perimeter of a square will be the sum of its four sides. Perimeter of square= side+side+side+side

But, because all the four sides of a square are equal, the formula for its perimeter will be;

P= a×a×a×a

P= 4×a

P= 4a, where a is the length of side

Or

P = 4 × side

Perimeter of square

For example, let us calculate the perimeter of a square of each side 7 cm.

The formula for the perimeter of a square is P = 4a, where a = length of each side of square.

Therefore, the perimeter of the square is, P = 4 x 7cm = 28cm

Also read: Perimeter and Area of circle 

---

Things to remember

• Square is quadrilateral with equal sides and angles.
• The diagonals of a square are equal and bisect each other at 90 degrees.
• The perimeter of a square is given by 4×side.
• A square has all the properties of a rectangle, except that it has equal sides.
• All the four angles of a square are 90 degrees.
• A square can be considered as a regular polygon.

Also read: Parallel perpendicular axes theorem

---