# How to calculate the diagonal length of a square

Diagonal of a Square Calculator

1. For the first idea, use the Pythagorean Theorem: where a and b are the side lengths of the square and c is the length of the diagonal. 2. If you know that ALL squares can be made into two special right triangles such that their angles are , then there's a . You can use Pythagorean Theorem to calculate the length of the diagonal of a square. This theorem shows that if you have a right triangle, the length of the hypotenuse is the square root of the sum of the square of the sides. The hypotenuse is the side which lies opposite of .

The diagonal divides the square into two triangles, which have side lengths in the ratio of. Therefore, the diagonal is the side length. If square represents a grassy area in the middle of your college campus, what is the shortest distance from point to point?

There are two pretty easy ways to solve this problem, both of which require you to see that this is actually a triangle question. The first method is the fastest. If you can recognize that the diagonal of a square makes a triangle, you can then recall that triangles have side lengths with ratios of.

In this what is the best website to buy air jordans, we want to solve for the diagonal, which is the hypotenuse of the triangle it forms, so we are solving for :. So again, we get. One side of a square has a length of.

What is the length of the diagonal of the square? By definition, all four sides of a square are the same length. So if one side has a length ofthe length and width of the square are both. The diagonal of the square is just the hypotenuse of a right triangle with the length and width as the other two sides, so we can use the Pythagorean Theorem to calculate the length of the diagonal:.

A circle is inscribed in a square. The diagonal of the square iswhat is the area of the circle? From what we are told, we can figure out the side of the square with this simple formula:where is the diagonal of the square and is the length of the side. So the length of the side of our square will be 2. Therefore the radius of the circle will be half that, or 1. Now that we now the radius, we can calculate the area of the circlewhere is the radius of the circle.

A square is inscribed in a circle. The circle has an area ofwhat is the ratio of the area of the square to the area of the circle? To get the area of the square we need to figure out, the length of the side.

Which is possible by calculating the diameter of the circle, which is in fact the diagonal of the square. We can do as follows:. We now know that the diagonal of the square is 4 as well, with the formulawhere is the length of the diagonal and is the length of the side of the square, we can figure out the length of the side, which is. Therefore, the area is the square of the side or 8.

The final ratio that we are looking for is or. The area of the square is. What can i buy with kohls cash is the circumference of the semicircle?

From the given area of the square we can figure out the length of the side of this square, which is the square root of the area, or 7. Using the formula for the diagonal of the square,where is the length of the diagonal, and the length of the side. Therefore, the length of the diagonal is. In this case since the square is inscribed in the circle, the diameter of the circle is equal to the diagonal of the square.

Therefore, we can find the circumference of the circleor. We just need to divide the result by 2 since we only want the circumference of the semicircle and also add the length of the diagonal, which "closes" the semicircle. The final answer is.

Find the length of the diagonal of a square whose side length is. To find the length of the diagonal, you can either use the pythagorean theorem or realize that the diagonal of a square is really the hypotenuse of a right isosceles triangle.

Therefore, using the short cut, you know that the diagonal is the side length times. Thus, the answer is:. If you've found an issue with this question, please let us know. With the help of the community we can continue to improve our educational resources.

If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available how to treat bursitis in ball of foot means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney. Hanley Rd, Suite St. Louis, MO We are open Saturday and Sunday! Subject optional. Home Embed. Email address: Your name:. A square has a side length of 3, how long is the diagonal of the square?

Possible Answers:. Correct answer:. Explanation : The diagonal divides the square into two triangles, which have side lengths what kind of wine is prosecco the ratio of. Report an Error. Given square FGHI below, solve for the following:. Explanation : There are two pretty easy ways how to clean a car properly solve this problem, both of which require you to see that this is actually a triangle question.

Therefore: The second way to solve this problem is to use Pythagorean Theorem: where and are leg lengths of a triangle and the length of the hypotenuse. In this case, we want to solve for the diagonal, which is the hypotenuse of the triangle it forms, so we are solving for : So again, we get. Explanation : By definition, all four sides of a square are the same length. Explanation : From what we are told, we can figure out the side of the square with this simple formula:where is the diagonal of the square and is the length of the side.

Explanation : To get the area of the square we need to figure out, the length of the side. We can do as follows: therefore the radius is 2 and the diameter is 4. Explanation : From the given area of the square we can figure out the length of the side of this square, which is the square root of the area, or 7. Explanation : To find the length of the diagonal, you can either use the pythagorean theorem or realize that the diagonal of a square is really the hypotenuse of a right isosceles triangle.

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The line stretching from one corner of the square or rectangle to the opposite corner through the center of the figure is known as the diagonal. Any square that has two diagonals are equal in length to each other. To find the length of the diagonal of a square when the area is given, take the square . Sep 30,  · How to Square up a Lay Out. Establish two parallel lines for the the width; Establish a starting point for the length on one of the lines; Mark the length down one of the lines from the starting point; Mark the diagonal on the other line from the same starting point; Mark the length down the line from the diagonal mark.

Side in the square below has a length of What is the length of the diagonal? Diagonal forms a triangle with adjacent sides. Since this is a square we know this is a right triangle and we can use the Pythagorean Theorem to determine the length of. Sides of length form each of the legs and is the hypotenuse.

So the equation looks like this:. Solve for. A man wants to build a not-quite-regulation softball field on his property and finds that he only has enough room to make the distance between home plate and first base 44 feet. How far nearest foot will it be from home plate to second base, assuming he builds it to that specification? Note: the four bases are the vertices of a perfect square, with the bases called home plate, first base, second base, third base, in that order.

The path from home plate to first base is a side of a perfect square; the path from home plate to second base is a diagonal. As two sides and a diagonal form a triangle, the diagonal measures as long as a side. The distance to second base from home is times the distance to first base:. A square lot has an area of 1, square meters.

To the nearest meter, how far is it from one corner to the opposite corner? A square is also a rhombus, so its area can be calculated as one half the product of its diagonals:. Since ,. The diagonal line cuts the square into two equal triangles.

Their hypotenuse is the diagonal of the square, so we can solve for the hypotenuse. We need to use the Pythagorean Theorem: , where a and b are the legs and c is the hypotenuse. Find the length of the diagonal of a square that has side lengths of cm.

For the first idea, use the Pythagorean Theorem: , where a and b are the side lengths of the square and c is the length of the diagonal. If you know that ALL squares can be made into two special right triangles such that their angles are , then there's a formula you could use:. Let's say that your side length of the square is "a". Then the diagonal of the square or the hypotenuse of the right triangle will be. We can break up the square into two equal right triangles.

The diagonal of the sqaure is then the hypotenuse of these two triangles. The perimeter of a square is units. How many units long is the diagonal of the square? From the perimeter, we can find the length of each side of the square. The side lengths of a square are equal by definition therefore, the perimeter can be rewritten as,.

Then we use the Pythagorean Theorme to find the diagonal, which is the hypotenuse of a right triangle with each leg being a side of the square. Find the length of the diagonal of the square with a side length of.

The diagonal of a square is also a hypotenuse of a right triangle with the side lengths as legs of the triangle. Find the length of the diagonal of a square with side lengths of. If you've found an issue with this question, please let us know. With the help of the community we can continue to improve our educational resources.

If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors. Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.

Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney. Hanley Rd, Suite St. Louis, MO We are open Saturday and Sunday! Subject optional. Home Embed.

Email address: Your name:. Possible Answers:. Correct answer:. Explanation : Diagonal forms a triangle with adjacent sides. So the equation looks like this: Solve for We can simplify this to. Report an Error. Explanation : The path from home plate to first base is a side of a perfect square; the path from home plate to second base is a diagonal. Explanation : A square is also a rhombus, so its area can be calculated as one half the product of its diagonals: , where is the common diagonal length.

The distance between opposite corners is about 49 meters. Find the length of the square's diagonal. Possible Answers: None of the other answers are correct. Explanation : The diagonal line cuts the square into two equal triangles. The two legs have lengths of 8. Plug this in and solve for c:. Explanation : You can do this problem in two different ways that lead to the final answer: 1. Pythagorean Theorem 2. Special Triangles 1.

If you know that ALL squares can be made into two special right triangles such that their angles are , then there's a formula you could use: Let's say that your side length of the square is "a".

The perimeter of a square is What is the length of its diagonal? Therefore, we can use the Pythagorean Theorem to solve for the diagonal:. Explanation : From the perimeter, we can find the length of each side of the square. The side lengths of a square are equal by definition therefore, the perimeter can be rewritten as, Then we use the Pythagorean Theorme to find the diagonal, which is the hypotenuse of a right triangle with each leg being a side of the square.

Explanation : The diagonal of a square is also a hypotenuse of a right triangle with the side lengths as legs of the triangle. Use the Pythagorean Theorem to find the length of the diagonal. For the square given in the question,. Copyright Notice. View Tutors. Christopher Certified Tutor. Tracy Certified Tutor. Cheryl Certified Tutor. University of West Georgia, Masters Report an issue with this question If you've found an issue with this question, please let us know.

Do not fill in this field. Louis, MO Or fill out the form below:. Company name. Copyright holder you represent if other than yourself.

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed. I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law. This notification is accurate. I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process. Your Full Name. Phone Number.

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