# 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:

$a=6 \ \\ b=4 \ \\ A=a \cdot \ b=6 \cdot \ 4=24 \ \\ u=\sqrt{ a^2+b^2 }=\sqrt{ 6^2+4^2 } \doteq 2 \ \sqrt{ 13 } \doteq 7.2111 \ \\ r=u/2=7.2111/2 \doteq \sqrt{ 13 } \doteq 3.6056 \ \\ B=\pi \cdot \ r^2=3.1416 \cdot \ 3.6056^2 \doteq 40.8407 \ \\ x=A/B=24/40.8407 \doteq 0.5876 \ \\ p=100 \cdot \ x=100 \cdot \ 0.5876 \doteq 58.7649 \doteq 58.765 \%$

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