Rog-sadee

Rog-sadee jechuun danaa ji’oomeetirii sarara qajeelaa sadii fi guttiyyoo(vertex) sadii irraa hojjetame dha.

Shallaggii naannoo roga sadii

Rog-sadee

Dheerinni cinaachaa roga sadii a, b fi c yoo ta’u kofoon α, β fi γ dha.	: 1.1. $s=a+b+c$ $\frac{a}{\sin \alpha }=\frac{b}{\sin \beta }=\frac{c}{\sin \gamma }.$ $c^2=a^2+b^2-2ab\cos (\gamma )$ $b^2=a^2+c^2-2ac\cos (\beta )$ $a^2=b^2+c^2-2bc\cos (\alpha )$ $\alpha =\arccos \left(\frac{b^2+c^2-a^2}{2bc}\right)$ $\beta =\arccos \left(\frac{a^2+c^2-b^2}{2ac}\right)$ $\gamma =\arccos \left(\frac{a^2+b^2-c^2}{2ab}\right)$

Shallaggii bal’ina roga saddeetii

$\mathrm{A}\mathrm{r}\mathrm{e}\mathrm{a}=\frac{1}{2}bh$

: 1.1. $\mathrm{A}\mathrm{r}\mathrm{e}\mathrm{a}=\frac{1}{2}bh$ Bal’inni bal’ina, b cinaacha kamiyyuu roga saddeetii agarsiisa, h immoo olka’iinsa cinaacha kana irraa gara golee faallaatti perpendikulaariin kaafame agarsiisa. $Area=\frac{1}{2}ab\sin \gamma =\frac{1}{2}bc\sin \alpha =\frac{1}{2}ca\sin \beta$ $Area=\frac{1}{2}ab\sin (\alpha +\beta )=\frac{1}{2}bc\sin (\beta +\gamma )=\frac{1}{2}ca\sin (\gamma +\alpha ).$ $Area=\frac{b^2(sin\alpha )(sin(\alpha +\beta ))}{2sin\beta }$ $Area=\frac{a^2}{2(cot\beta +\cot \gamma )}=\frac{a^2(sin\beta )(sin\gamma )}{2sin(\beta +\gamma )}$ $Area=\sqrt{s(s-a)(s-b)(s-c)}$ As $s=\frac{a+b+c}{2}$ Mee guddinni kofa 3 walakkaa naannoo ta’uu isaa haa hubannu $Area=\frac{1}{4}\sqrt{(a^2+b^2+c^2{)}^2-2(a^4+b^4+c^4)}$ $Area=\frac{1}{4}\sqrt{2(a^2{b}^2+a^2{c}^2+b^2{c}^2)-(a^4+b^4+c^4)}$ $Area=\frac{1}{4}\sqrt{(a+b-c)(a-b+c)(-a+b+c)(a+b+c)}.$

Gosoota Rogsadee

• 
  Rogsadee rogqixaa
• 
  Rog-sadee lamqixaa(isosceles)
• 
  Rog-sadee mitqixaa

Rogsadeen kofa sirri kan ballinni kofa saa 90 madaalkofa(digrii)

Rogsadeen kofqoree kan ballinni kofa isaa >90 madaalkofa(digrii)

Rogsadeen kofa jufunfula kan ballinni kofa saa <90 madaalkofa(digrii)

Rogsadee kofasirri	Rogsadee jufunfula (Obtuse)	Rogsadee kofqoree(acute)
	$\underset{}{\underbrace{}}$
	Habalakaa (Obliikii)