Paraleelogram

En Paraleelogram as en sjauerhuk, diar en Rütj liket, man a sidjen san ei aaltumaal likelung. A sidjen, diar jinauer lei, san oober likelung.

Tekst üüb Öömrang

Paraleelogram mä
• huken A, B, C, D
• sidjen a = c, b = d
• winkler α = γ, β = δ
• hööchde h_a ≠ h_b
• diagonaalen e, f

Bereegnangen

Bereegnangsformeln
Areaal	${\displaystyle A=a\cdot h_{a}=b\cdot h_{b}=\left|\left|{\overrightarrow {AB}}\times {\overrightarrow {AD}}\right|\right|}$ ${\displaystyle A=a\cdot b\cdot \sin(\alpha )=a\cdot b\cdot \sin(\beta )={\frac {e\cdot f\cdot \sin(\theta )}{2}}}$
Amfaadang	${\displaystyle U=2\cdot a+2\cdot b=2\cdot (a+b)}$
Banenwinkler	${\displaystyle \alpha =\gamma ,\quad \beta =\delta ,\quad \alpha +\beta =180^{\circ }}$
Hööchde	${\displaystyle h_{a}=b\cdot \sin(\alpha )}$
	${\displaystyle h_{b}=a\cdot \sin(\beta )}$
Lengde faan a Diagonaalen (efter Kosinussats)	${\displaystyle {\begin{array}{ccl}e&={\sqrt {a^{2}+b^{2}-2\cdot a\cdot b\cdot \cos(\beta )}}\\&={\sqrt {a^{2}+b^{2}+2\cdot a\cdot b\cdot \cos(\alpha )}}\end{array}}}$
	${\displaystyle {\begin{array}{ccl}f&={\sqrt {a^{2}+b^{2}-2\cdot a\cdot b\cdot \cos(\alpha )}}\\&={\sqrt {a^{2}+b^{2}+2\cdot a\cdot b\cdot \cos(\beta )}}\end{array}}}$
Paraleelogramliknang	${\displaystyle e^{2}+f^{2}=2\cdot (a^{2}+b^{2})}$

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 Commonskategorii: Paraleelogram – Saamlang faan bilen of filmer