Substituting these values into the formula, we obtain. The formula for the length of the diagonal of a rectangle Example 1:Ī rectangle has length of 6m and a width of 2m. Evaluating this, d = √40 and therefore the diagonal is approximately 6.32m long. For example, the diagonal of a rectangle of length 6m and width 2m is given by d = √(6² + 2²). The formula to find the diagonal of a rectangle is d = √(l² + w²), where l is the length and w is the width of the rectangle. Formula to Find the Diagonal of a Rectangle The diagonal is the hypotenuse of the triangle formed by dividing the rectangle in two. Given the length and width of a rectangle, the diagonal is found by squaring these values, adding them and then finding the square root of this. This means that the rectangle is divided into two right-angled triangles from which Pythagoras’ Theorem can be used The calculator also assumes that in all measurements, the length is the longer measurement.The diagonals of a rectangle are equal in length and divide the rectangle into two congruent triangles. With all of these formulas, the α refers to the angle between the diagonal measurements. Length and width: d = √ (l² + w²) Area and width: d = √ (A²/w² + w²) Area and length: d = √ (A²/l² + l²) Perimeter and width: d = √ (2w² - P*w + P²/4) Perimeter and length: d = √ (2l² - P*l + P²/4)) Angle and width: d = w / sin(α/2) Angle and length: or d = l / cos(α/2) Perimeter and area: d = √ (P² - 2*A) Perimeter and angle: d = P / (2*sin(α/2) + 2*cos(α/2)) Angle and area: d = √ (2 * A / sin(α)) Below, you will see what each formula looks like when you have the following information. With these formulas, you can now identify various other methods – depending on the measurements you receive, for working out the diagonal of a rectangle. Rectangle perimeter: P = 2 x w + 2 x l 2. Sometimes, you may only get two measurements, and you have to use different formulas to work it out from there.įirstly, we’ll cover the three equations you will need for the rectangle’s perimeter, area, and the circumcircle radius.ġ. What is the Formula for Finding the Diagonal of a Rectangle? You are not always going to have all the appropriate measurements for working out the diagonal of a rectangle handed to you on a plate. You can also use the diagonal of a rectangle calculator to measure in various units using SI and imperial. Then, to get the exact formula for finding the diagonal of a rectangle, take a square root. You also use the Pythagorean theorem to receive an approximate diagonal measurement: All triangles will have a length ( l) and width ( w) and a hypotenuse of ( d) for the length. The formula involves dividing your rectangle into its two congruent right triangles – with at least one 90-degree angle. How Do You Find the Diagonal of a Rectangle? Using a diagonal of a rectangle calculator makes the entire process effortless as long as you have other measurements, but you can also use the diagonal of a rectangle formula. You may not know that a square is also a particular type of rectangle. A rectangle also has two intersecting diagonals which are also the same length. From this name, you can determine that a rectangle is a quadrilateral with four right angles – two of which are parallel and of equal length. The word rectangle is derived from two Latin words – rectus (meaning right or proper) and angulus (meaning angle). All of these components help to create the shape itself. To determine the diagonal of a rectangle, you can use the length, width, angle, circumcircle, area, and perimeter measurements. Fortunately, as long as you have the other parameters of a rectangle, you can find the diagonal measurement – and others - using this calculator tool. When you want to find out the diagonal of a rectangle, it can be a complicated process to do so by hand.
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