Koostame sirgete võrrandid:

AB: $$y = kx + b$$ $$3 = 2k + b$$ $$6 = -k + b$$ $$3 - 2k = 6 + k$$ $$-3k = 3$$ $$k = -1$$ $$b=5$$ $$y = -x + 5$$

BC: $$y = kx + b$$ $$6 = -k + b$$ $$-1 = -2k + b$$ $$6 + k = -1 + 2k$$ $$7 = k$$ $$b=13$$ $$y = 7x + 13$$

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

DA: $$y = kx + b$$ $$2 = -5k + b$$ $$3 = 2k + b$$ $$2 + 5k = 3 - 2k$$ $$7k = 1$$ $$k = \frac{1}{7}$$ $$b = \frac{19}{7}$$ $$y = \frac{1}{7}x + \frac{19}{7}$$

Leiame ristküliku külgede pikkused, ümbermõõdu ja pindala:

$$\vec{AB} = B - A = (-1; 6) - (2; 3) = (-3; 3)$$ $$\vec{BC} = C - B = (-2; -1) - (-1; 6) = (-1; -7)$$ $$\vec{CD} = D - C = (-5; 2) - (-2; -1) = (-3; 3)$$ $$\vec{DA} = A - D = (2; 3) - (-5; 2) = (7; 1)$$ $$\vert{\vec{AB}}\vert = \sqrt{(-3)^2 + 3^2} = \sqrt{18}$$ $$\vert{\vec{BC}}\vert = \sqrt{(-1)^2 + (-7)^2} = \sqrt{50}$$ $$\vert{\vec{CD}}\vert = \sqrt{(-3)^2 + 3^2} = \sqrt{18}$$ $$\vert{\vec{DA}}\vert = \sqrt{7^2 + 1^2} = \sqrt{50}$$ $$P = \vert{\vec{AB}}\vert + \vert{\vec{BC}}\vert + \vert{\vec{CD}}\vert + \vert{\vec{DA}}\vert = 2\sqrt{18} + 2\sqrt{50}$$ $$S = \sqrt{p(p-a)(p-b)(p-c)}$$ $$p = \frac{a + b + c}{2}$$ $$p = \frac{\sqrt{18} + \sqrt{50} + \sqrt{18} + \sqrt{50}}{2}$$ $$S = 30$$

Leiame ringjoone võrrandi:

$$(x - \frac{1}{2})^ 2 + (y - \frac{9}{2}) ^ 2 = \frac{81}{4}$$

Leiame ringi pindala, mis ei ole ristküliku poolt kaetud:

$$\frac{81\pi}{4} - 30$$