# Circle and rectangle

A rectangle with sides of 11.7 cm and 175 mm is described by circle. What is its length? Calculate the content area of the circle described by this circle.

Correct result:

x =  66.133 cm
S =  348.041 cm2

#### Solution:

$a=11.7 \ \text{cm} \ \\ b=175/10=\dfrac{ 35 }{ 2 }=17.5 \ \text{cm} \ \\ u=\sqrt{ a^2+b^2 }=\sqrt{ 11.7^2+17.5^2 } \doteq 21.0509 \ \text{cm} \ \\ r=u/2=21.0509/2 \doteq 10.5254 \ \text{cm} \ \\ x=2 \pi \cdot \ r=2 \cdot \ 3.1416 \cdot \ 10.5254=66.133 \ \text{cm}$
$S=\pi \cdot \ r^2=3.1416 \cdot \ 10.5254^2=348.041 \ \text{cm}^2$

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