The formula to calculate the Area of a Rhombus given its inradius and obtuse angle is:
\[ A = \frac{4 \cdot r_i^2}{\sin(\angle_{\text{Obtuse}})} \]
The Area of a Rhombus is the amount of two-dimensional space occupied by the rhombus. The inradius is the radius of the circle which is inscribed inside the rhombus. The obtuse angle is the angle inside the rhombus which is greater than 90 degrees.
Let's assume the following values:
Using the formula:
\[ A = \frac{4 \cdot 3^2}{\sin(2.3561944901919)} \approx 50.9116882454088 \, \text{square meters} \]
The Area of the Rhombus is approximately 50.9116882454088 square meters.
| Inradius (meters) | Area of Rhombus (square meters) |
|---|---|
| 2.5 | 35.355339059311639 |
| 2.6 | 38.240334726551474 |
| 2.7 | 41.238467478781104 |
| 2.8 | 44.349737316000535 |
| 2.9 | 47.574144238209755 |
| 3 | 50.911688245408783 |
| 3.1 | 54.362369337597599 |
| 3.2 | 57.926187514776217 |
| 3.3 | 61.603142776944630 |
| 3.4 | 65.393235124102844 |