how to find the diagonal of a square

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The diagonal of a square is the line stretching from one corner of the square to the opposite corner. To find the diagonal of a square, you can use the formula ${\displaystyle d=s{\sqrt {2}}}$ , where ${\displaystyle s}$ equals one side length of the square. Sometimes, however, you might be asked to find the length of the diagonal given another value, such as the perimeter or area of the square. In these instances it is necessary to use different formulas first, so that you can determine the side length before using the diagonal formula.

1. 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

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3. 3

   Plug the side length of the square into the formula. Make sure you are substituting for the variable ${\displaystyle s}$ .

   • For example, if the square has a side length of 5 centimeters, set up the formula like this:
     ${\displaystyle d=5{\sqrt {2}}}$

4. 4

   Multiply the length of the side by $$ 2 {\displaystyle {\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 ${\displaystyle {\sqrt {2}}}$ to 1.414.

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1. 1

2. 2

   Plug the length of the perimeter into the formula. Make sure you are substituting for the variable ${\displaystyle P}$ .

   • For example, if the perimeter of the square is 20 centimeters, your formula will look like this:
     ${\displaystyle 20=4s}$

3. 3

   Solve for $$ s {\displaystyle s} . To do this, divide each side of the equation by 4. This will give you the length of one side of the square.

4. 4

5. 5

   Plug the side length of the square into the formula. Make sure you are substituting for the variable ${\displaystyle s}$ .

   • For example, if the square has a side length of 5 centimeters, set up the formula like this:
     ${\displaystyle d=5{\sqrt {2}}}$

6. 6

   Multiply the length of the side by $$ 2 {\displaystyle {\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 ${\displaystyle {\sqrt {2}}}$ to 1.414.

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1. 1

2. 2

   Plug the area measurement into the formula. Make sure you are substituting for the variable ${\displaystyle A}$ .

   • For example, if the area of the square is 25 square centimeters, your formula will look like this:
     ${\displaystyle 25=s^{2}}$

3. 3

   Solve for $$ s {\displaystyle s} . To do this, find the square root of the area. This will give you the length of one side of the square. To find the square root, use a calculator. If you need help calculating the square root by hand, read Calculate a Square Root by Hand.

4. 4

5. 5

   Plug the side length of the square into the formula. Make sure you are substituting for the variable ${\displaystyle s}$ .

   • For example, if the square has a side length of 5 centimeters, set up the formula like this:
     ${\displaystyle d=5{\sqrt {2}}}$

6. 6

   Multiply the length of the side by $$ 2 {\displaystyle {\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 ${\displaystyle {\sqrt {2}}}$ to 1.414.

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Add New Question

• Question

  How do I calculate the sides of a square if the diagonal is given?

  

  First square the diagonal's length. Divide that by two. Then find the square root of that last number. That's the side of the square.

• Question

  How do you find the diagonal of a 24 x 24 foot square?

  

  Since you know the length of one side (24) you can use method 1: d = s x sqrt*2 d = 24 x 1.414 d = 33.936

• Question

  How do I identify a right angle?

  

  You'll know if an angle is right angle if it is 90 degrees.

• Question

  What is the diagonal of a 15 x 7 foot area?

  

  A 15 x 7 foot area is not a square. You can still find the length of the diagonal by using the Pythagorean Theorem: 15^2 + 7^2 = c^2, where c is the length of the diagonal. Thus: 15^2 + 7^2 = c^2 225 + 49 = c^2 274 = c^2 sqrt*274 = sqrt*c^2 16.55 = c

• Question

  Diagonal measurement of a 4 inch square

  

  Since you know the length of one side of the square (4), you can use method 1. d = s x sqrt*2 d = 4 x 1.414 d = 5.565

• Question

  A square is 8 feet by 8 feet. What is the diagonal distance from corner to corner?

  

  Since you know the length of one side (8 feet), you can use method 1: d = s x sqrt*2 d = 8 x 1.414 d = 11.312

• Question

  How do I calculate the area of a square?

  

  Multiply the length by the width. If they only give you the length or the width, multiply that same number by itself, (for example: the length is 5 in, 5*5=25in2). This process only works with squares. If the problem only gives you the area and the length or width, you divide the area by the length or width.

• Question

  How to find diagonals when I only have the area?

  

  Double the area. Then find the square root of that number. That's the diagonal.

• Question

  How can I find the diagonal length of a square that is 213 meters by 200 meters?

  

  This is not a square. However, you can still use Pythagorean's Theorem to find the length of the diagonal. Diagonal length = D = sq. root of (213^2 + 200^2) = sq. root (45369 + 40000) = sq. root (85369) = 292.2.

• Question

  How do I square a number?

  

  Multiply it by itself. For example, 6² = (6)(6) = 36.

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Article SummaryX

To calculate a diagonal of a square, multiply the length of one of the square's sides by the square root of 2. If you don't know the length of one side, you can find it by plugging the square's perimeter into the formula: perimeter = 4s, where s is the length of one side. If you don't know the perimeter, you can still find the length of one side by plugging the square's area into the formula: area = s^2, where s is the length of one side. For help solving these formulas, keep reading!

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how to find the diagonal of a square

Source: https://www.wikihow.com/Calculate-a-Diagonal-of-a-Square

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