Dalam Geometri, oktagon atau segi delapan (atau astakona) adalah sebuah segi banyak atau poligon yang mempunyai delapan sisi. Sebuah segi delapan beraturan mempunyai simbol Schläfli {8}.
L = 2 cot π 8 a 2 = 2 ( 1 + 2 ) a 2 ≃ 4.828 a 2 . {\displaystyle L=2\cot {\frac {\pi }{8}}a^{2}=2(1+{\sqrt {2}})a^{2}\simeq 4.828\,a^{2}.} Diagonald 1 = 2 ⋅ r r = 4 + 2 2 ⋅ a ≈ 2,613 ⋅ a {\displaystyle d_{1}=2\cdot r_{\mathrm {r} }={\sqrt {4+2{\sqrt {2}}}}\cdot a\approx 2{,}613\cdot a} d 2 = 2 ⋅ r l = ( 1 + 2 ) ⋅ a ≈ 2,414 ⋅ a {\displaystyle d_{2}=2\cdot r_{\mathrm {l} }=(1+{\sqrt {2}})\cdot a\approx 2{,}414\cdot a} Jari jari lingkaranr l = 1 + 2 2 ⋅ a ≈ 1,207 ⋅ a {\displaystyle r_{\mathrm {l} }={\frac {1+{\sqrt {2}}}{2}}\cdot a\approx 1{,}207\cdot a} Radiusr r = 1 2 ⋅ 4 + 2 2 ⋅ a ≈ 1,307 ⋅ a {\displaystyle r_{\mathrm {r} }={\frac {1}{2}}\cdot {\sqrt {4+2{\sqrt {2}}}}\cdot a\approx 1{,}307\cdot a} Sudut tengahα = 360 ∘ 8 = 45 ∘ {\displaystyle \alpha ={\frac {360^{\circ }}{8}}=45^{\circ }} Sudut interiorδ = 180 ∘ − α = 135 ∘ {\displaystyle \delta =180^{\circ }-\alpha =135^{\circ }} Segi delapan biasa dapat dibangun dengan batang gunung berapi . Kita membutuhkan dua belas batang ukuran 4, tiga batang ukuran 5 dan dua batang ukuran 6. Setiap sisi oktagon biasa memotong setengah sudut kanan di tengah lingkaran yang menghubungkan simpul-simpulnya. Dengan demikian luasnya dapat dihitung sebagai jumlah dari 8 segitiga sama kaki, yang mengarah ke hasil: Luas = 2 a 2 ( 2 + 1 ) {\displaystyle {\text{Luas}}=2a^{2}({\sqrt {2}}+1)}untuk segi delapan sisi a . |
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Perhatikan prisma segi delapan di bawah ini.
Titik sudut prisma segi-delapan diatas adalah titik A,B,C,D,E,F,G,H,I,J,K,L,M,N,O dan P yang berjumlah 16 titik.
Atau secara matematis banyak titik sudut pada prisma segi-n dapat dicari menggunakan rumus
banyak titik sudut=2n
Sehingga banyak titik sudut pada prisma segi-delapan adalah
banyak titik sudut==2×816
Jadi, banyaknya titik sudut prisma segi-delapan adalah 16.