The formula to calculate the Area of a Parallelogram given Diagonals and Obtuse Angle between Diagonals is:
\[ A = \frac{1}{2} \cdot d_{Long} \cdot d_{Short} \cdot \sin(\angle_{d(Obtuse)}) \]
Where:
The Area of a Parallelogram is the total quantity of plane enclosed by the boundary of the Parallelogram.
The Long Diagonal of a Parallelogram is the length of the line joining the pair of acute angle corners of a Parallelogram.
The Short Diagonal of a Parallelogram is the length of the line joining the pair of obtuse angle corners of a Parallelogram.
The Obtuse Angle between the Diagonals of a Parallelogram is the angle made by the diagonals of the Parallelogram which is greater than 90 degrees.
Let's assume the following values:
Using the formula:
\[ A = \frac{1}{2} \cdot 18 \cdot 9 \cdot \sin(2.2689280275922) \]
Evaluating:
\[ A = \frac{1}{2} \cdot 18 \cdot 9 \cdot \sin(2.2689280275922) \]
The Area of the Parallelogram is approximately 62.0495998926595 Square Meter.
| Long Diagonal of Parallelogram (Meter) | Short Diagonal of Parallelogram (Meter) | Obtuse Angle between Diagonals of Parallelogram (Radian) | Area of Parallelogram (Square Meter) |
|---|---|---|---|
| 16 | 8 | 2 | 58.195035316843629 |
| 16 | 8 | 2.1 | 55.245399465527917 |
| 16 | 8 | 2.2 | 51.743769844453766 |
| 16 | 8 | 2.3 | 47.725133579310082 |
| 16 | 8 | 2.4 | 43.229643555273640 |
| 16 | 9 | 2 | 65.469414731449078 |
| 16 | 9 | 2.1 | 62.151074398718904 |
| 16 | 9 | 2.2 | 58.211741075010487 |
| 16 | 9 | 2.3 | 53.690775276723841 |
| 16 | 9 | 2.4 | 48.633348999682845 |
| 16 | 10 | 2 | 72.743794146054540 |
| 16 | 10 | 2.1 | 69.056749331909899 |
| 16 | 10 | 2.2 | 64.679712305567207 |
| 16 | 10 | 2.3 | 59.656416974137599 |
| 16 | 10 | 2.4 | 54.037054444092050 |
| 17 | 8 | 2 | 61.832225024146354 |
| 17 | 8 | 2.1 | 58.698236932123415 |
| 17 | 8 | 2.2 | 54.977755459732123 |
| 17 | 8 | 2.3 | 50.707954428016961 |
| 17 | 8 | 2.4 | 45.931496277478246 |
| 17 | 9 | 2 | 69.561253152164653 |
| 17 | 9 | 2.1 | 66.035516548638839 |
| 17 | 9 | 2.2 | 61.849974892198645 |
| 17 | 9 | 2.3 | 57.046448731519085 |
| 17 | 9 | 2.4 | 51.672933312163025 |
| 17 | 10 | 2 | 77.290281280182938 |
| 17 | 10 | 2.1 | 73.372796165154270 |
| 17 | 10 | 2.2 | 68.722194324665153 |
| 17 | 10 | 2.3 | 63.384943035021202 |
| 17 | 10 | 2.4 | 57.414370346847804 |
| 18 | 8 | 2 | 65.469414731449078 |
| 18 | 8 | 2.1 | 62.151074398718904 |
| 18 | 8 | 2.2 | 58.211741075010487 |
| 18 | 8 | 2.3 | 53.690775276723841 |
| 18 | 8 | 2.4 | 48.633348999682845 |
| 18 | 9 | 2 | 73.653091572880214 |
| 18 | 9 | 2.1 | 69.919958698558773 |
| 18 | 9 | 2.2 | 65.488208709386797 |
| 18 | 9 | 2.3 | 60.402122186314323 |
| 18 | 9 | 2.4 | 54.712517624643198 |
| 18 | 10 | 2 | 81.836768414311351 |
| 18 | 10 | 2.1 | 77.688842998398627 |
| 18 | 10 | 2.2 | 72.764676343763114 |
| 18 | 10 | 2.3 | 67.113469095904804 |
| 18 | 10 | 2.4 | 60.791686249603558 |
| 19 | 8 | 2 | 69.106604438751816 |
| 19 | 8 | 2.1 | 65.603911865314402 |
| 19 | 8 | 2.2 | 61.445726690288851 |
| 19 | 8 | 2.3 | 56.673596125430720 |
| 19 | 8 | 2.4 | 51.335201721887444 |
| 19 | 9 | 2 | 77.744929993595790 |
| 19 | 9 | 2.1 | 73.804400848478707 |
| 19 | 9 | 2.2 | 69.126442526574948 |
| 19 | 9 | 2.3 | 63.757795641109560 |
| 19 | 9 | 2.4 | 57.752101937123378 |
| 19 | 10 | 2 | 86.383255548439763 |
| 19 | 10 | 2.1 | 82.004889831642998 |
| 19 | 10 | 2.2 | 76.807158362861060 |
| 19 | 10 | 2.3 | 70.841995156788400 |
| 19 | 10 | 2.4 | 64.169002152359312 |
| 20 | 8 | 2 | 72.743794146054540 |
| 20 | 8 | 2.1 | 69.056749331909899 |
| 20 | 8 | 2.2 | 64.679712305567207 |
| 20 | 8 | 2.3 | 59.656416974137599 |
| 20 | 8 | 2.4 | 54.037054444092050 |
| 20 | 9 | 2 | 81.836768414311351 |
| 20 | 9 | 2.1 | 77.688842998398627 |
| 20 | 9 | 2.2 | 72.764676343763114 |
| 20 | 9 | 2.3 | 67.113469095904804 |
| 20 | 9 | 2.4 | 60.791686249603558 |
| 20 | 10 | 2 | 90.929742682568175 |
| 20 | 10 | 2.1 | 86.320936664887370 |
| 20 | 10 | 2.2 | 80.849640381959006 |
| 20 | 10 | 2.3 | 74.570521217672010 |
| 20 | 10 | 2.4 | 67.546318055115066 |