Koʻpburchak, trapetsiya va uchburchak yuzi

🟢 — masalani tezlashtiradi · 🟡 — ilg'or daraja · 🔵 — chuqur o'rganish (olimpiada darajasi)

Boshqa foydali formulalar

• Ko'pburchak ichki burchaklari yig'indisi: $S = 180°(n - 2)$
• Trapetsiya yuzi: $A = \frac{1}{2}(a + b)h$

🟢 Uchburchak yuzi (uchlari orqali)

$S = \frac{1}{2}\left|\,x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)\,\right|$

• Uch nuqta bir chiziqda ⇔ $S = 0$

🔵 Ko'pburchak yuzi (shnurok formulasi)

Uchlari ketma-ket $(x_1, y_1), \dots, (x_n, y_n)$ bo'lsa:

$S = \frac{1}{2}\left|\sum_{i=1}^{n} (x_i\,y_{i+1} - x_{i+1}\,y_i)\right| \qquad (x_{n+1} = x_1,\; y_{n+1} = y_1)$

🔵 Uchburchak yuzi — boshqa formulalar

$p = \dfrac{a + b + c}{2}$ — yarim perimetr:

$S = \sqrt{p(p - a)(p - b)(p - c)} \;\;\text{(Geron)} \qquad S = \frac{abc}{4R} \qquad S = rp \;\;(r \text{ — ichki aylana radiusi})$