ሶስት ማእዘን

${\displaystyle s=a+b+c}$

${\displaystyle {\frac {a}{\sin \alpha }}={\frac {b}{\sin \beta }}={\frac {c}{\sin \gamma }}.}$

${\displaystyle c^{2}\ =a^{2}+b^{2}-2ab\cos(\gamma )}$

${\displaystyle b^{2}\ =a^{2}+c^{2}-2ac\cos(\beta )}$

${\displaystyle a^{2}\ =b^{2}+c^{2}-2bc\cos(\alpha )}$

${\displaystyle \alpha =\arccos \left({\frac {b^{2}+c^{2}-a^{2}}{2bc}}\right)}$

${\displaystyle \beta =\arccos \left({\frac {a^{2}+c^{2}-b^{2}}{2ac}}\right)}$

${\displaystyle \gamma =\arccos \left({\frac {a^{2}+b^{2}-c^{2}}{2ab}}\right)}$

${\displaystyle \mathrm {Area} ={\frac {1}{2}}bh}$

Area ሚለው ስፋትን ሲያመለክት፣ b የሚለው ማንኛውንም የ3 ማእዘን ጎን ሲሆን ፣ h ደግሞ ከዚህ ጎን እስከ በትይዩው ወዳለው ማእዘን በስትክክል የሚሳል ቁመትን ይመለከታል።

${\displaystyle Area={\frac {1}{2}}ab\sin \gamma ={\frac {1}{2}}bc\sin \alpha ={\frac {1}{2}}ca\sin \beta }$

${\displaystyle Area={\frac {1}{2}}ab\sin(\alpha +\beta )={\frac {1}{2}}bc\sin(\beta +\gamma )={\frac {1}{2}}ca\sin(\gamma +\alpha ).}$

${\displaystyle Area={\frac {b^{2}(sin\alpha )(sin(\alpha +\beta ))}{2sin\beta }}}$

${\displaystyle Area={\frac {a^{2}}{2(cot\beta +\cot \gamma )}}={\frac {a^{2}(sin\beta )(sin\gamma )}{2sin(\beta +\gamma )}}}$

${\displaystyle Area={\sqrt {s(s-a)(s-b)(s-c)}}}$

እዚህ ላይ ${\displaystyle s={\frac {a+b+c}{2}}}$ የ 3 ማዕዘኑ መጠነ ዙርያ ግማሽ እንደሆነ እናስተውል

${\displaystyle Area={\frac {1}{4}}{\sqrt {(a^{2}+b^{2}+c^{2})^{2}-2(a^{4}+b^{4}+c^{4})}}}$

${\displaystyle Area={\frac {1}{4}}{\sqrt {2(a^{2}b^{2}+a^{2}c^{2}+b^{2}c^{2})-(a^{4}+b^{4}+c^{4})}}}$

${\displaystyle Area={\frac {1}{4}}{\sqrt {(a+b-c)(a-b+c)(-a+b+c)(a+b+c)}}.}$