Circumradius of Rectangle given Area and Length Calculator

Circumradius of Rectangle Formula:

\[ r_c = \frac{1}{2} \times \sqrt{l^2 + \left(\frac{A}{l}\right)^2} \]

Circumradius of Rectangle:

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1. What is the Circumradius of Rectangle?

The Circumradius of Rectangle is the radius of the circle which contains the Rectangle with all the vertices of Rectangle are lying on the circle. It represents the distance from the center of the rectangle to any of its vertices.

2. How Does the Calculator Work?

The calculator uses the circumradius formula:

\[ r_c = \frac{1}{2} \times \sqrt{l^2 + \left(\frac{A}{l}\right)^2} \]

Where:

\( r_c \) — Circumradius of Rectangle (m)
\( l \) — Length of Rectangle (m)
\( A \) — Area of Rectangle (m²)

Explanation: The formula calculates the radius of the circumscribed circle by finding half the length of the rectangle's diagonal, which can be derived from the Pythagorean theorem using the length and width (where width = area/length).

3. Importance of Circumradius Calculation

Details: Calculating the circumradius is important in geometry and various engineering applications where understanding the spatial relationships between rectangles and their circumscribed circles is necessary for design and analysis purposes.

4. Using the Calculator

Tips: Enter the length of the rectangle and its area. Both values must be positive numbers. The calculator will compute the circumradius of the rectangle's circumscribed circle.

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between circumradius and rectangle dimensions?
A: The circumradius equals half the length of the rectangle's diagonal, connecting opposite vertices.

Q2: Can this formula be used for squares?
A: Yes, for squares (where length = width), the formula simplifies to \( r_c = \frac{l\sqrt{2}}{2} \).

Q3: What are the units of circumradius?
A: The circumradius has the same units as the rectangle's dimensions (meters, centimeters, etc.).

Q4: How is this different from inradius?
A: The circumradius is for the circle passing through all vertices, while the inradius (for rectangles that are squares) is for the circle inscribed within the shape.

Q5: What if the area is zero?
A: The calculator requires positive values for both length and area. A zero area would indicate a degenerate rectangle.