1. What is Circumradius of Rectangle?

The circumradius of a rectangle is the radius of the circle which contains the rectangle with all the vertices of the rectangle lying on the circle. For any rectangle, the circumradius is equal to half the length of the diagonal.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( rc \) — Circumradius of Rectangle (m)
• \( A \) — Area of Rectangle (m²)
• \( \angle dl \) — Angle between Diagonal and Length of Rectangle (rad)

Explanation: This formula calculates the circumradius using the area of the rectangle and the angle between its diagonal and length, employing trigonometric functions to derive the result.

3. Importance of Circumradius Calculation

Details: Calculating the circumradius is important in geometry and various engineering applications where circular patterns or arrangements involving rectangles are needed, such as in architectural design and mechanical engineering.

4. Using the Calculator

Tips: Enter the area of the rectangle in square meters and the angle between the diagonal and length in radians. Ensure the angle is between 0 and π/2 radians (0-90 degrees).

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between circumradius and diagonal?
A: The circumradius of a rectangle is exactly half the length of its diagonal.

Q2: Can this formula be used for squares?
A: Yes, since a square is a special type of rectangle, this formula applies to squares as well.

Q3: What are the units for circumradius?
A: The circumradius has units of length (meters, centimeters, etc.), the same as the units used for the area input.

Q4: Why use radians instead of degrees?
A: The trigonometric functions in the formula work with radians. If you have degrees, convert them to radians first (radians = degrees × π/180).

Q5: What if the angle is 0 or 90 degrees?
A: At 0 degrees, the formula becomes undefined. At 90 degrees, the rectangle degenerates into a line, and the circumradius calculation may not be meaningful.