How to Find the Area of a Square

Co-authored by David Jia

Last Updated: July 24, 2023 Fact Checked

Finding the area of a square is easy as long as you know the length of its side, perimeter, or diagonal. Here's how to do it.

Method 1

Method 1 of 3:

Using the Length of a Side

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Let's say you're working with a square with a side length of 3 centimeter (1.2 in). Write it down.
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 cm².^{[1]
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Be sure to state your answer in square units. Then you're done.^{[2]
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- Squaring the side of a square is the same thing as multiplying the square's height times its base.

Method 2

Method 2 of 3:

Using a Known Diagonal

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Area = (diagonal^2)/2.^{[3]
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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 cm².
Continuing the calculation, 25 cm² is divided by 2. This gives 12.5 cm². You're done.

Method 3

Method 3 of 3:

Using a Known Perimeter

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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).^{[4]
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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)² = 25 centimeter (9.8 in).²^{[5]
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Question

If the area of the square is 9 cm, what is the volume of the cube?

Donagan

Top Answerer

Take the square root of 9 and cube it. The answer will be expressed in cm³.

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Question

What is the formula to calculate the area of an isosceles triangle that has a base and equal sides?

Community Answer

Multiply the length of the base of the triangle by 0.5, and then multiply the length from the base to the highest point of the triangle. A = 0.5 x b x h.

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Question

A square is 1 cm by 1 cm; what is the area?

Donagan

Top Answerer

Multiply 1 cm by 1 cm: the area is 1 square cm.

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