# Diagonal of a Rectangle Calculator

**Diagonal of a Rectangle Calculator: **Students can learn the geometric concepts from here. This Page describes the simple steps to calculate the rectangle diagonal length, formulas that helps you to find the diagonal of a rectangle and some example questions.

Ex: length = 1000 And width = 500

**Here are some samples of Diagonal of a Rectangle calculations**

Make use of free online calculator tool to find the diagonal of a rectangle easily and instantly. All you need to do is provide length and width of the rectangle in the given input sections and tap on the diagonal button to see the accurate result in a short span of time.

## Diagonal of a Rectangle Formulas

Below given are the formulas that are useful to calculate the diagonal length of a rectangle. Utilize these formulas whenever required to solve the questions effortlessly.

1. When length, width of the rectangle is given

Diagonal length d = √(l² + w²)

2. If length/ width and area of a rectangle is given, then

Diagonal of a rectangle d = √(A² / l² + l²) or d = √(A² / w² + w²)

3. Length/ width and perimeter of rectangle are known.

Diagonal d = √(2l² - P * l + P² / 4) or d = √(2w² - P * w + P² / 4)

4. Given length/ width and angle between then

diagonal d = w / sin(α/2) or l / cos(α/2)

5. Given area and angle

Diagonal d = √(2 * A / sin(α))

6. If area and perimeter of rectangle are available

Diagonal of a rectangle d = √(P² - 2*A)

7. When perimeter and angle is given,

Diagonal d = P / (2*sin(α/2) + 2*cos(α/2))

8. When circum radius of rectangle is given,

Diagonal d = 2 * r

Where,

d is the length of diagonal of a rectangle

r is the circum radius of the rectangle

α is the angle

P is the rectangle perimeter

l is the length of rectangle

w is the width of the rectangle

A is the rectangle area

### Steps to Find Diagonal Length of a Rectangle

Get the step by step process to calculate the length of diagonal of a rectangle from the following section.

- Observe the length, width of the rectangle from the question.
- Perform the square of both parameters.
- Add the sum of length and width squares.
- Apply square root to the resultant value to check the diagonal of a rectangle.

### Examples on Rectangle Diagonal

**Example 1: **One side of a rectangle is 5 inches and another is 9 inches. How many inches long is the rectangle's diagonal?

**Solution: **

Given that,

Length of rectangle l = 9 inches

Width of rectangle w = 5 inches

Diagonal of a rectangle d = √(l² + w²)

By substituting the given values in the formula

d = √(9² + 5²)

= √(81 + 25) = √(106)

= 10.29

∴ The length of diagonal of a rectangle =is 10.29 inches.

**Example 2: **Find the rectangle diagonal length? If rectangle area is 25 cm² and width is 4 cm?

**Solution: **

Given that,

Area of rectangle A = 25 cm²

Width w = 4 cm

Diagonal d = √(A² / w² + w²)

= √(25² / 4² + 4²)

= √(625 / 16 + 16)

= √(39.06 + 16) = √(55.06)

= 7.42

∴ Rectangle diagonal is 7.42 cm.

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### FAQs on Diagonal of a Rectangle Calculator

**1. What is the formula to calculate the diagonal of a rectangle?**

If we draw any one diagonal in a rectangle, it will form a right angle triangle. By using the Pythagorean theorem, diagonal² = length² + width². So, diagonal = √(length² + width²).

**2. How many diagonals can be drawn in a rectangle?**

It is possible to draw only two diagonals for a rectangle.

**3. What is the length of diagonal of a rectangle?**

A diagonal divides the rectangle into two right angle triangles with sides equal to the sides of a rectangle and diagonal is the hypotenuse.

**4. Does diagonals of a rectangle measures equal length?**

Yes, two diagonals of a rectangle are equal and bisect each other at the midpoint of diagonal.