Leiame kolmnurga külgede pikkused:

$$AB = \sqrt{(1 - (-3))^2 + (2 - (-1))^2} = 5$$ $$BC = \sqrt{(1 - (-3))^2 + (-4 - (-1))^2} = 5$$ $$AC = \sqrt{(1 - 1)^2 + (2 - (-4))^2} = 6$$

Kuna kolmnurga külgede pikkused on erinevad, siis kolmnurk ABC ei ole võrdkülgne.

Leiame kolmnurga ABC pindala kasutades Heroni valemit:

$$S=\sqrt{p(p-a)(p-b)(p-c)}$$ $$p=\frac{a+b+c}{2}$$ $$p=\frac{5+5+6}{2}=\frac{16}{2}=8$$ $$S=\sqrt{8(8-5)(8-5)(8-6)}=12$$

Leiame külgede BA ja BC keskpunktid:

$$R = \left(\frac{1 + (-3)}{2}; \frac{2 + (-1)}{2}\right) = (-1; \frac{1}{2})$$ $$S = \left(\frac{1 + 1}{2}; \frac{2 + (-4)}{2}\right) = (1; -1)$$

Leiame kolmnurga RBS pindala:

$$RB = \sqrt{(-1 - 1)^2 + (\frac{1}{2} - (-1))^2} = \frac{5}{2}$$ $$RS = \sqrt{(1 - (-1))^2 + (-1 - \frac{1}{2})^2} = \frac{5}{2}$$ $$BS = \sqrt{(1 - (-1))^2 + (-1 - \frac{1}{2})^2} = \frac{5}{2}$$ $$p = \frac{RB + RS + BS}{2} = \frac{\frac{5}{2} + \frac{5}{2} + \frac{5}{2}}{2} = \frac{15}{4}$$ $$S = \sqrt{p(p - RB)(p - RS)(p - BS)} \newline = \sqrt{\frac{15}{4} \cdot \frac{5}{4} \cdot \frac{5}{4} \cdot \frac{5}{4}} \newline = \sqrt{\frac{1875}{256}} \newline = \frac{5\sqrt{15}}{8}$$

Kolmnurkade ABC ja RBS pindalade suhe on:

$$\frac{S_{ABC}}{S_{RBS}} = \frac{12}{\frac{5\sqrt{15}}{8}} \newline = \frac{12 \cdot 8}{5\sqrt{15}} \newline = \frac{96}{5\sqrt{15}} \newline = \frac{32\sqrt{15}}{25} $$