The formula to calculate the Area of a Parallelogram given its Heights and Obtuse Angle is:
\[ \text{Area} = \frac{\text{Height to Long Edge} \times \text{Height to Short Edge}}{\sin(\text{Obtuse Angle})} \]
Where:
The Area of Parallelogram is the total quantity of plane enclosed by the boundary of the parallelogram.
Let's assume the following values:
Using the formula:
\[ \text{Area} = \frac{5 \times 8}{\sin(2.3561944901919)} \]
Evaluating:
\[ \text{Area} = \frac{40}{0.7071067811865476} \]
\[ \text{Area} = 56.5685424948986 \]
The Area of the Parallelogram is 56.5685424948986 square meters.
| Height to Long Edge (m) | Height to Short Edge (m) | Obtuse Angle (radians) | Area (square meters) |
|---|---|---|---|
| 5 | 5 | 1.5 | 25.062782606168 |
| 5 | 5 | 2 | 27.493754257365 |
| 5 | 5 | 2.5 | 41.773038638967 |
| 5 | 10 | 1.5 | 50.125565212336 |
| 5 | 10 | 2 | 54.987508514731 |
| 5 | 10 | 2.5 | 83.546077277934 |
| 5 | 15 | 1.5 | 75.188347818504 |
| 5 | 15 | 2 | 82.481262772096 |
| 5 | 15 | 2.5 | 125.319115916901 |
| 10 | 5 | 1.5 | 50.125565212336 |
| 10 | 5 | 2 | 54.987508514731 |
| 10 | 5 | 2.5 | 83.546077277934 |
| 10 | 10 | 1.5 | 100.251130424673 |
| 10 | 10 | 2 | 109.975017029462 |
| 10 | 10 | 2.5 | 167.092154555868 |
| 10 | 15 | 1.5 | 150.376695637009 |
| 10 | 15 | 2 | 164.962525544192 |
| 10 | 15 | 2.5 | 250.638231833802 |
| 15 | 5 | 1.5 | 75.188347818504 |
| 15 | 5 | 2 | 82.481262772096 |
| 15 | 5 | 2.5 | 125.319115916901 |
| 15 | 10 | 1.5 | 150.376695637009 |
| 15 | 10 | 2 | 164.962525544192 |
| 15 | 10 | 2.5 | 250.638231833802 |
| 15 | 15 | 1.5 | 225.565043455513 |
| 15 | 15 | 2 | 247.443788316289 |
| 15 | 15 | 2.5 | 375.957347750703 |