How Do You Find the Perimeter and Area of a Square?

Now, let’s look at one type of quadrilateral, the square. In a square, all the angles are $90$°, and all the sides have the same length. As all the angles are $90$°, the square is a special case of a rectangle.

Perimeter of a Square

To find the perimeter of a square, you only need to know the length of one of the sides. As the sides are all of equal length, you can just multiply the length of one side by 4.

Formula

PerimeterofaSquare

$\begin{array}{llll}\hfill P& =4\cdot \text{side}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =4\cdot s\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

Example 1

Calculate the perimeter of the following square:

We use the formula and find:

 $P=4\cdot 3\phantom{\rule{0.17em}{0ex}}\text{cm}=12\phantom{\rule{0.17em}{0ex}}\text{cm}$

Area of a Square

When finding the area of a square, you multiply the square’s height by its width. As the height and the width are the same in a square, you just multiply the length of one side by itself.

Formula

AreaofaSquare

$\begin{array}{llll}\hfill A& =\text{side}\cdot \text{side}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =s\cdot s\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & ={s}^{2}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

Example 2

Find the area of the following square:

The area is equal to

 $A=4\phantom{\rule{0.17em}{0ex}}\text{cm}\cdot 4\phantom{\rule{0.17em}{0ex}}\text{cm}=16\phantom{\rule{0.17em}{0ex}}{\text{cm}}^{2}$

The area is thus $16$ cm2.