1. Square
A square is a special quadrilateral where all four sides are equal and each interior angle is \(90^\circ\). Because all sides have the same length, the boundary of a square is simply four equal segments repeated in a loop.
The length of each side is usually represented by \(a\).
1.1. Definition of Perimeter
The perimeter is the total length around the boundary of a 2D shape. For a square, this means adding all four equal sides.
Since every side has the same length, the calculation becomes very simple.
2. Perimeter Formula
Let the length of each side of the square be \(a\). Since there are four equal sides, the perimeter is:
\( P = 4a \)
2.1. Working of the Perimeter Formula
A square has:
- side 1 = \(a\)
- side 2 = \(a\)
- side 3 = \(a\)
- side 4 = \(a\)
So the perimeter becomes:
\( P = a + a + a + a = 4a \)
3. Examples
Look at these simple examples to understand how the formula is used.
3.1. Example 1
A square has side length \(a = 7\,\text{cm}\). Its perimeter is:
\( P = 4a = 4 \times 7 = 28\,\text{cm} \)
3.2. Example 2
A playground is in the shape of a square with each side equal to \(15\,\text{m}\). Its boundary length is:
\( P = 4a = 4 \times 15 = 60\,\text{m} \)