Desribed circle to rectangle

Rectangle with sides 6 cm and 4 cm was circumscribed circle. What part of the content of the circle determined by the circumscribed circle occupies a rectangle? Express in perctentages(%).

Result

p =  58.765 %

Solution:

a=6 b=4 A=a b=6 4=24 u=a2+b2=62+42=2 137.2111 r=u/2=7.2111/2=133.6056 B=π r2=3.1416 3.6056240.8407 x=A/B=24/40.84070.5876 p=100 x=100 0.587658.7649=58.765%a = 6 \ \\ b = 4 \ \\ A = a \cdot \ b = 6 \cdot \ 4 = 24 \ \\ u = \sqrt{ a^2+b^2 } = \sqrt{ 6^2+4^2 } = 2 \ \sqrt{ 13 } \doteq 7.2111 \ \\ r = u/2 = 7.2111/2 = \sqrt{ 13 } \doteq 3.6056 \ \\ B = \pi \cdot \ r^2 = 3.1416 \cdot \ 3.6056^2 \doteq 40.8407 \ \\ x = A/B = 24/40.8407 \doteq 0.5876 \ \\ p = 100 \cdot \ x = 100 \cdot \ 0.5876 \doteq 58.7649 = 58.765 \%



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