Perimeter of Rectangle given Breadth and Circumradius Calculator

Formula

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

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

Where:

\(P\) is the Perimeter of Rectangle (measured in meters).
\(b\) is the Breadth 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.

Breadth of Rectangle is any one of the pair of parallel sides which are shorter 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:

Breadth of Rectangle (b) = 6 meters
Circumradius of Rectangle (rc) = 5 meters

Using the formula:

\[ P = 2 \left( 6 + \sqrt{(4 \cdot 5^2) - 6^2} \right) \]

Evaluating:

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

The Perimeter of Rectangle is approximately 28 meters.

Conversion Chart

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Breadth (b) (meters)	Circumradius (rc) (meters)	Perimeter (P) (meters)