Formeln von verschiedenen Figuren
Trapez
Seiten
| \[ a = c + x + y \] | \[ b = \frac{h}{\sin(\beta)} \] |
| \[ d = \sqrt{h^2 + y^2} \] | \[ h = \sin({\alpha}) \cdot d \] |
| \[ c = a - x - y \ \ \ \text{oder} \ \ \ c = \sqrt{h^2 + x^2} \] | |
| \[ x = \sqrt{d^2 - h^2} \] | \[ y = \sqrt{b^2 - h^2} \] |
Winkel
| \[ \alpha = 180° - \delta \] | \[ \gamma = 180° - \beta \] |
| \[ \beta = 180° - \gamma \] | \[ \delta = 180° - \alpha \] |
Rechteck
Seiten
| \[a = d \cdot \sin\left(\frac{f}{2}\right)\] | \[b = \sqrt{d^2 - a^2}\] |
| \[d = \sqrt{a^2 - b^2}\] |
Winkel
| \[\phi = \arctan\left(\frac{b}{a}\right) \] |
Raute
Seiten
| \[ a = \sqrt{\left(\frac{e}{2}\right)^2 + \left(\frac{f}{2}\right)^2 } \] | |
| \[ f = 2 \cdot a \cdot \sin\left(\frac{\alpha}{2}\right) \] | \[ e = 2 \cdot a \cdot \cos\left(\frac{\alpha}{2}\right) \] |
Winkel
| \[ \alpha = 2 \cdot \arctan\left(\frac{\frac{f}{2}}{\frac{e}{2}}\right) \] | \[ \beta = 180° - \alpha \] |
Deltoid
Seiten
| \[ e_1 = \sqrt{a^2 - \left(\frac{f}{2}\right)^2} \] | \[ e_2 = e - e_1 \] |
| \[ b = \sqrt{e_2^2 - \left(\frac{f}{2}\right)^2} \] |
Winkel
| \[ \alpha = \arcsin\left(\frac{\frac{f}{2}}{a}\right) \cdot 2 \] | \[ \gamma = \arcsin\left(\frac{\frac{f}{2}}{b}\right) \cdot 2 \] |
| \[ \beta + \delta = 360° - \alpha - \gamma \] |