Perimeter of Rectangle given Length and Circumradius Calculator

Formula

The formula to calculate the Perimeter of Rectangle (P) is:

\[ P = 2 \left( l + \sqrt{(4 \cdot rc^2) - l^2} \right) \]

Where:

\(P\) is the Perimeter of Rectangle (measured in meters).
\(l\) is the Length of Rectangle (measured in meters).
\(rc\) is the Circumradius of Rectangle (measured in meters).

Definition

The Perimeter of Rectangle is the total length of all the boundary lines of the Rectangle.

Length of Rectangle is any one of the pair of parallel sides which are longer than the remaining pair of parallel sides.

Circumradius of Rectangle is the radius of the circle which contains the Rectangle with all the vertices of Rectangle lying on the circle.

How to calculate Perimeter of Rectangle

Let's assume the following values:

Length of Rectangle (l) = 8 meters
Circumradius of Rectangle (rc) = 5 meters

Using the formula:

\[ P = 2 \left( 8 + \sqrt{(4 \cdot 5^2) - 8^2} \right) \]

Evaluating:

\[ P \approx 28 \, \text{meters} \]

The Perimeter of Rectangle is approximately 28 meters.

Conversion Chart

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Length (l) (meters)	Circumradius (rc) (meters)	Perimeter (P) (meters)