How to Calculate a Diagonal of a Square

Step-by-Step Guide

1. 1

   Step 1: Find the length of one side of the square.

   This will probably be given to you.
   
   If you are working with a square in the real world, use a ruler or piece of measuring tape to find the length.
   
   Since all four sides of the square are the same length, you can use any side of the square.
   
   If you do not know the length of one side of the square, you cannot use this method.
   
   For example, you might want to find the length of the diagonal of a square that has sides 5 centimeters long.
2. 2

   Step 2: Set up the formula d=s2{\displaystyle d=s{\sqrt {2}}}.

   In the formula d{\displaystyle d} equals the length of the diagonal and s{\displaystyle s} equals one side of the square.This formula is derived from the Pythagorean Theorem (a2+b2=c2){\displaystyle a^{2}+b^{2}=c^{2})}.
   
   A diagonal divides a square into two congruent right triangles, thus, you can use the side lengths of the square to find the length of the diagonal (which would be the hypotenuse of the right triangle). , Make sure you are substituting for the variable s{\displaystyle s}.
   
   For example, if the square has a side length of 5 centimeters, set up the formula like this:d=52{\displaystyle d=5{\sqrt {2}}} , This will give you the length of the diagonal.
   
   It’s best to perform the calculation on a calculator, so that you can get a more precise result.
   
   If you don’t have a calculator, you can round 2{\displaystyle {\sqrt {2}}} to
   1.414.
   
   For example, if you are calculating the diagonal of a 5-centimeter square, your formula will look like this:d=52{\displaystyle d=5{\sqrt {2}}}d=7.07{\displaystyle d=7.07}So, the diagonal of the square is
   7.07 centimeters long.
3. 3

   Step 3: Plug the side length of the square into the formula.

4. 4

   Step 4: Multiply the length of the side by 2{\displaystyle {\sqrt {2}}}.

Detailed Guide

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