How to Find the Area of a Square

Using the Length of a Side

Write it down. Let's say you're working with a square with a side length of 3 centimeter (1.2 in). Write it down.

Understand the formula for the area of a square(Area=side^2). To calculate the area of any rectangle, you need to multiply its length by width. But since all squares have equal length sides, you can just multiply the distance by itself. If the length of a side of a square is 3 centimeter (1.2 in), then you just have to square 3 centimeter (1.2 in) to find the area of a square. 3 centimeter (1.2 in) x 3 centimeter (1.2 in) = 9 cm.

Be sure to state your answer in square units. Then you're done. Squaring the side of a square is the same thing as multiplying the square's height times its base.

Using a Known Diagonal

Take the measurement of the length of the diagonal of the square.

Understand the formula for the area using a known diagonal. Area = (diagonal^2)/2.

Multiply the length of this diagonal's measurement by itself. Square the length of the diagonal. Let's say you're working with a square with a diagonal that is 5 centimeter (2.0 in) long. Now, square this number. 5 centimeter (2.0 in) x 5 centimeter (2.0 in) = 25 cm.

Divide the current number by 2. Continuing the calculation, 25 cm is divided by 2. This gives 12.5 cm. You're done.

Using a Known Perimeter

Multiply the perimeter by 1/4 to find the length of a side. This is the same as dividing the perimeter by 4. Since there are four sides to a square and each side is of equal length, you can find the length of a square just by dividing the perimeter by 4. Let's say the perimeter of the square you're working with is 20 centimeter (7.9 in). Just multiply 20 centimeter (7.9 in) by 1/4: 20 centimeter (7.9 in) x 1/4 = 5 centimeter (2.0 in). You know that the length of a side of the square is 5 centimeter (2.0 in).

Multiply the length of the side by itself. Square the length of the side. Now that you know that the length of a side is 5 centimeter (2.0 in), you can square it to get the area of the square. Area = (5 cm) = 25 centimeter (9.8 in).

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