# 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

### 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.