The formula to calculate the area of a rectangle given its length and circumradius is:
\[ A = l \cdot \sqrt{(4r_c^2) - l^2} \]
Where:
The area of a rectangle is the total quantity of plane enclosed by the boundary of the rectangle.
The length of the rectangle is any one of the pair of parallel sides which are longer than the remaining pair of parallel sides.
The circumradius of the rectangle is the radius of the circle which contains the rectangle with all its vertices lying on the circle.
Let's assume the following values:
Using the formula:
\[ A = 8 \cdot \sqrt{(4 \cdot 5^2) - 8^2} \approx 48 \, \text{square meters} \]
The area is approximately 48 square meters.
| Length (meters) | Circumradius (meters) | Area (square meters) |
|---|---|---|
| 6 | 4 | 31.7490 |
| 6 | 5 | 48.0000 |
| 6 | 6 | 62.3538 |
| 7 | 4 | 27.1109 |
| 7 | 5 | 49.9900 |
| 7 | 6 | 68.2276 |
| 8 | 4 | 0.0000 |
| 8 | 5 | 48.0000 |
| 8 | 6 | 71.5542 |