The formula to calculate the Area of a Rectangle given its breadth and circumradius is:
\[ \text{Area} = \text{Breadth} \cdot \sqrt{(4 \cdot \text{Circumradius}^2) - \text{Breadth}^2} \]
The Area of a Rectangle is the total quantity of plane enclosed by the boundary of the rectangle. The breadth of the rectangle is any one of the pair of parallel sides which are shorter than the remaining pair of parallel sides. The circumradius of the rectangle is the radius of the circle which contains the rectangle with all the vertices of the rectangle lying on the circle.
Let's assume the following values:
Using the formula:
\[ \text{Area} = 6 \cdot \sqrt{(4 \cdot 5^2) - 6^2} \approx 48 \, \text{square meters} \]
The Area is approximately 48 square meters.
| Breadth (meters) | Circumradius (meters) | Area (square meters) |
|---|---|---|
| 5 | 4 | 31.224989991991990 |
| 5 | 4.5 | 37.416573867739416 |
| 5 | 5 | 43.301270189221938 |
| 5 | 5.5 | 48.989794855663561 |
| 5 | 6 | 54.543560573178567 |
| 5.5 | 4 | 31.952112606211188 |
| 5.5 | 4.5 | 39.181468834131266 |
| 5.5 | 5 | 45.934055993347684 |
| 5.5 | 5.5 | 52.394536928958537 |
| 5.5 | 6 | 58.659504771179243 |
| 6 | 4 | 31.749015732775089 |
| 6 | 4.5 | 40.249223594996216 |
| 6 | 5 | 48.000000000000000 |
| 6 | 5.5 | 55.317266743757322 |
| 6 | 6 | 62.353829072479584 |
| 6.5 | 4 | 30.313981922538652 |
| 6.5 | 4.5 | 40.462173693463384 |
| 6.5 | 5 | 49.395723499104655 |
| 6.5 | 5.5 | 57.681777885221258 |
| 6.5 | 6 | 65.566283255954048 |
| 7 | 4 | 27.110883423451920 |
| 7 | 4.5 | 39.597979746446661 |
| 7 | 5 | 49.989998999799951 |
| 7 | 5.5 | 59.396969619669989 |
| 7 | 6 | 68.227560413662744 |