How To Find Length Of Diagonal Of 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 discover the diagonal of a square, you can utilise the formula ${\displaystyle d=due south{\sqrt {2}}}$ , where ${\displaystyle s}$ equals 1 side length of the square. Sometimes, still, you might be asked to find the length of the diagonal given another value, such every bit the perimeter or area of the foursquare. In these instances it is necessary to use different formulas first, and so that you can decide the side length before using the diagonal formula.

1. 1

   Observe the length of one side of the foursquare. This will probably be given to you. If yous are working with a square in the real world, use a ruler or slice of measuring tape to detect the length. Since all iv sides of the square are the aforementioned length, you lot can use any side of the square. If you practice not know the length of one side of the square, you lot cannot use this method.

   • For example, you might want to find the length of the diagonal of a square that has sides five centimeters long.

2. 2

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3. three

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

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

4. 4

   Multiply the length of the side by $$ two {\displaystyle {\sqrt {2}}} . This will requite you the length of the diagonal. It'southward best to perform the calculation on a calculator, and then that yous can get a more than precise result. If you don't have a calculator, you can round ${\displaystyle {\sqrt {ii}}}$ to 1.414.

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1. one

2. 2

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

   • For instance, if the perimeter of the square is twenty centimeters, your formula volition look similar this:
     ${\displaystyle 20=4s}$

3. 3

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

4. 4

5. 5

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

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

6. half-dozen

   Multiply the length of the side past $$ 2 {\displaystyle {\sqrt {2}}} . This volition give you the length of the diagonal. Information technology's all-time to perform the adding on a calculator, and so that you lot can get a more precise event. If y'all don't have a figurer, 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 $$ southward {\displaystyle s} . To do this, observe the square root of the expanse. This volition give you the length of 1 side of the foursquare. To observe the foursquare root, use a calculator. If you need help computing 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 ${\displaystyle southward}$ .

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

6. six

   Multiply the length of the side past $$ 2 {\displaystyle {\sqrt {2}}} . This volition give you the length of the diagonal. *It's best to perform the calculation on a calculator, and so that you can get a more than precise consequence. If you don't have a calculator, you tin round ${\displaystyle {\sqrt {2}}}$ to i.414.

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Add New Question

• Question

  How exercise I calculate the sides of a foursquare if the diagonal is given?

  

  Kickoff foursquare the diagonal's length. Separate that by two. Then observe the square root of that last number. That'due south the side of the foursquare.

• Question

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

  

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

• Question

  How practice I identify a correct angle?

  

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

• Question

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

  

  A fifteen 10 vii foot area is non a square. You tin still notice 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^two = c^2 225 + 49 = c^2 274 = c^2 sqrt*274 = sqrt*c^two 16.55 = c

• Question

  Diagonal measurement of a iv inch square

  

  Since you know the length of one side of the square (iv), y'all tin can use method ane. d = s x sqrt*ii d = 4 ten ane.414 d = five.565

• Question

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

  

  Since you lot know the length of one side (8 anxiety), you can use method 1: d = southward x sqrt*two d = viii ten ane.414 d = 11.312

• Question

  How do I summate the surface area of a square?

  

  Multiply the length past the width. If they merely give you the length or the width, multiply that same number by itself, (for case: the length is 5 in, five*v=25in2). This process simply works with squares. If the problem only gives you lot the expanse and the length or width, you separate the area past the length or width.

• Question

  How to find diagonals when I only accept the area?

  

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

• Question

  How can I discover the diagonal length of a square that is 213 meters past 200 meters?

  

  This is not a square. All the same, y'all tin nonetheless apply Pythagorean's Theorem to find the length of the diagonal. Diagonal length = D = sq. root of (213^ii + 200^2) = sq. root (45369 + 40000) = sq. root (85369) = 292.2.

• Question

  How do I square a number?

  

  Multiply it by itself. For instance, 6² = (half dozen)(6) = 36.

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Commodity Summary Ten

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

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

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