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Area of a square from the diagonal
The properties of a square allows you to use the diagonal to find the area.
A square has four equal sides and each corner forms a 90-degree angle.
The diagonal cuts each corner into two 45 degree angles.
As a result, you have a 45 45 90 triangle with the diagonal as the hypotenuse.
In order to find the area we need the length of at least one side.
The hypotenuse of a 45 45 90 triangle equals x√2 and the other two sides equal x
We can use this information to find the area of a square.
For example, if the diagonal of a square equals 6 let's find the area.
Set the diagonal equal to x√2
6 = √2
Divide both sides by √2 = 3√2
This equals x or the length of one side
Next, you can plug this into the area formula of a square
3√2 x 3√2 or Side x Side in order to find the area of the square.
3√2 x 3√2 = 18
Area of a square from a diagonal of 6 = 18 square units