Do you need calculate the side of a square? Below you will find all the ways to get how long one of the sides of this four-sided figure is and if there is any other method, let us know and we will add it.
Many geometry problems ask us to calculating the side of a square from its diagonalso you can use our calculator and get the result automatically. For the rest of the cases we will explain it theoretically.
How to calculate the side of a square by knowing the diagonal
If we are asked to calculate the side from the diagonal of a squarethe procedure to follow is based on the Theorem of Pythagoras. If you want to know more about this theorem, visit the link we just left you.
If we adapt the Pythagorean Theorem to a square having all sides equalwe are left with the following formula:
d2 = a2 + a2 = 2a2
That formula basically tells us that the diagonal of the square squared is equal to twice the side of the square squared. Now what we have to do is to clear from there the unknown 'a' which is the one we are interested in for calculating the side of the square from the diagonal:
a = diagonal/√2
To better understand the procedure, let's see it with a solved example.
Calculate the side of a square whose diagonal is 12
They give us a square whose diagonal measures 12 centimeters and we are asked to find how long its sides are. To do this, we use the formula seen in the previous point and we have that:
a = 12 cm / √2 = 8,48528 cm
If we want to check that the value we have obtained is correct, it is enough to resort to the Pythagorean Theorem and check that the initial formula is fulfilled:
d2 = 12 x 12 = 144
2a2= 2 x 8.48528 x 8.48528 = 144
As you can see, equality holds, so that we have calculated the sides of the square correctly. If the equality is not met by tenths or hundredths, you may be carrying over inaccuracies as a result of rounding.
How to calculate the side of a square having the area
The formula of the area of a square tells us that we must multiply side by side, that is:
Area of a square = side2
So for calculate the side of a square from its area we simply have to make the square root of its surface:
Side of square = √(area of square).
For example, if we are given a square with a surface area of 100cm2how long is its side?
l = √100 = 10 cm
It's easy, isn't it?
Calculate the side of a square inscribed in a circle
If we have a square inscribed in a circle of radius rwe can calculate the side with the following formula:
side = √2r2
For example, if we are given a square inscribed in a circle of 6 cm radius, how long is its side? To solve it we apply the above formula and we have that:
side = √2r2 = √(2 x 6 x 6 x 6) = √72 = 8,485 cm
If you have any doubts about how to calculate the side of a square using the methods described above or any other method not listed here, write us a comment and we will help you solve your questions.