Koostame võrrandi sirgele f(x):

$$k = \tan{45} = 1$$ $$5 = 3 + b$$ $$b=2$$ $$f(x) = x + 2$$

Koostame võrrandi sirgele g(x):

$$k_1 k_2 = -1$$ $$k_1 = 1$$ $$k_2 = -1$$ $$y=k_2 x + b$$ $$0 = -4 + b$$ $$b = 4$$ $$g(x) = -x + 4$$

Leiame punkti C, kus sirged omavahel lõikuvad:

$$f(x) = g(x)$$ $$x + 2 = -x + 4$$ $$2x = 2$$ $$x = 1$$ $$y = 1 + 2 = 3$$ $$C(1; 3)$$

Koostame võrrandi sirgele AB:

$$y=kx+b$$ $$5 = 3k + b$$ $$3 = k + b$$ $$5 - 3k = 3 - k$$ $$2 = 2k$$ $$k = 1$$ $$b = 2$$ $$y = x + 2$$

Leiame kolmnurga ABC ümbermõõdu ja pindala:

$$\vec{AB} = B - A = (4, 0) - (3, 5) = (1, -5)$$ $$\vec{BC} = C - B = (1, 3) - (4, 0) = (-3, 3)$$ $$\vec{AC} = C - A = (1, 3) - (3, 5) = (-2, -2)$$ $$\vert{\vec{AB}}\vert = \sqrt{1^2 + (-5)^2} = \sqrt{26}$$ $$\vert{\vec{BC}}\vert = \sqrt{(-3)^2 + 3^2} = \sqrt{18}$$ $$\vert{\vec{AC}}\vert = \sqrt{(-2)^2 + (-2)^2} = \sqrt{8}$$ $$P = \sqrt{26} + \sqrt{18} + \sqrt{8}$$ $$S = \sqrt{p(p-a)(p-b)(p-c)}$$ $$p = \frac{a + b + c}{2}$$ $$S = 6$$

Leiame küljele BC tõmmatud kõrguse:

$$S = \frac{1}{2}ah$$ $$h = \frac{2S}{a}$$ $$h = \frac{2 \cdot 6}{\sqrt{18}}$$ $$h = \frac{12}{3\sqrt{2}}$$ $$h = \frac{4}{\sqrt{2}}$$