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
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?
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)
∴ 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?
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)
∴ 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.