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 cm b=175/10=352=17.5 cm u=a2+b2=11.72+17.52≐21.0509 cm r=u/2=21.0509/2≐10.5254 cm x=2π⋅ r=2⋅ 3.1416⋅ 10.5254=66.133 cma=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=π⋅ r2=3.1416⋅ 10.52542=348.041 cm2S=\pi \cdot \ r^2=3.1416 \cdot \ 10.5254^2=348.041 \ \text{cm}^2

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