The formula to calculate the area of a rectangle given its diagonal and the acute angle between the diagonals is:
\[ \text{Area} = \frac{\text{Diagonal}^2 \cdot \sin(\text{Acute Angle})}{2} \]
The area of a rectangle is the total quantity of plane enclosed by the boundary of the rectangle. The acute angle between the diagonals of the rectangle is the angle made by the diagonals which is less than 90 degrees.
Let's assume the following values:
Using the formula:
\[ \text{Area} = \frac{10^2 \cdot \sin(1.2217304763958)}{2} \approx 46.9846 \, \text{square meters} \]
The area is approximately 46.9846 square meters.
| Diagonal (meters) | Acute Angle (radians) | Area (square meters) |
|---|---|---|
| 10 | 1.2217304763958 | 46.9846 |
| 12 | 1.0471975511966 | 62.3538 |
| 15 | 0.7853981633974 | 79.5495 |