To find the area of a square, you use the formula: Area = side × side = side² where "side" is the length of one side of the square. Since all sides of a square are equal, you simply multiply the length of one side by itself to get the area. The area is expressed in square units (e.g., square centimeters, square meters)

Examples:

• If the side length is 7 cm, the area is 7×7=49 cm27\times 7=49\text{ cm}^27×7=49 cm2

• If the side length is 8 inches, the area is 8×8=64 in28\times 8=64\text{ in}^28×8=64 in2

Alternative methods:

• If you know the diagonal ddd of the square, the area can be found using:

Area=d22\text{Area}=\frac{d^2}{2}Area=2d2​

For example, if the diagonal is 12 cm, the area is 1222=72 cm2\frac{12^2}{2}=72\text{ cm}^22122​=72 cm2

• If you know the perimeter PPP of the square, you can find the side by dividing the perimeter by 4, then square it to get the area:

side=P4,Area=(P4)2\text{side}=\frac{P}{4},\quad \text{Area}=\left(\frac{P}{4}\right)^2side=4P​,Area=(4P​)2

For example, if the perimeter is 32 units, the side is 32/4=832/4=832/4=8 units and the area is 82=648^2=6482=64 square units

In summary, the simplest and most common way to find the area of a square is to square the length of one of its sides.