In your experimentation, did you consider the case when all four sides of the rectangle are equal? That is, did you consider the case of a square? See what happens in this special case!

Question

Homi · Accepted Answer

A square is a special rectangle. All its four sides are equal.

Step 1 — Understanding a Square

Let us think about a rectangle. It has a length and a width. We can call the length $L$ . We can call the width $W$ . For a square, all four sides are equal. So, its length and width must be the same. Let us call this side length $s$ . So, $L = s$ . And $W = s$ .

Diagram 1

Step 2 — Perimeter of a Square

The perimeter of a rectangle is $2 \times (\text{length} + \text{width})$ . For a square, length is $s$ . Width is also $s$ . So, we put $s$ for length and $s$ for width.

$\text{Perimeter} = 2 \times (s + s)$

$= 2 \times (2s)$

$\boxed{\text{Perimeter} = 4s}$

Step 3 — Area of a Square

The area of a rectangle is $\text{length} \times \text{width}$ . For a square, length is $s$ . Width is also $s$ . So, we multiply $s$ by $s$ .

$\text{Area} = s \times s$

$\boxed{\text{Area} = s^2}$

Answer

When a rectangle becomes a square: Its length and width become equal. We can call this common side length $s$ . The perimeter becomes $4s$ . The area becomes $s \times s$ , or $s^2$ .

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