Content

• Necessities

The diagonal of a square is the line from one corner of that square to the opposite corner. To find the diagonal of a square, use the formula ${ displaystyle d = s { sqrt {2}}}$Find the length of one side of the square. This is probably given. If you're dealing with a real-world square, use a ruler or tape measure to determine the length. Since all four sides of the square are the same length, you can use any side of the square. If you don't know the sides of the square, you cannot use this method.

• For example, determine the length of the diagonal of a square with sides measuring 5 centimeters.

Write down the formula:${ displaystyle d = s { sqrt {2}}}$Enter the length of the side of the square in the formula. Make sure to substitute for the variable ${ displaystyle s}$Multiply the length of the side by 2{ displaystyle { sqrt {2}}}Write the formula for the perimeter of a square. The formula is ${ displaystyle P = 4s}$Plug the length of the outline into the formula. Make sure to fill in for the variable ${ displaystyle P}$Solve for s{ displaystyle s}Write the formula d=s2{ displaystyle d = s { sqrt {2}}}Plug the side length of the square into the formula. Make sure to substitute for the variable ${ displaystyle s}$Multiply the length of the side by 2{ displaystyle { sqrt {2}}}Write down the formula for the area of ​​a square. The formula is ${ displaystyle A = s ^ {2}}$Substitute the value for the area in the formula. Make sure to substitute for the variable ${ displaystyle A}$Solve for s{ displaystyle s}Write the formula d=s2{ displaystyle d = s { sqrt {2}}}Use the side length of the square in the formula. Make sure to substitute for the variable ${ displaystyle s}$Multiply the length of the side by 2{ displaystyle { sqrt {2}}}. This will give you the length of the diagonal. It is best to do this calculation with a calculator to get a more accurate result. If you don't have a calculator, get it around ${ displaystyle { sqrt {2}}}$ down to 1.414.

• For example, if you calculate the diagonal of a 5 centimeter square, your formula would look like this:
  ${ displaystyle d = 5 { sqrt {2}}}$
  ${ displaystyle d = 7.07}$
  So, the diagonal of the square is 7.07 centimeters.

Necessities

• Calculator