Annular area

The square with side a = 1 is inscribed and circumscribed by circles. Find the annular area.

Correct result:

S =  0.785

Solution:

a=1 r=a/2=1/2=12=0.5 R=2 a/2=2 1/20.7071  S1=π R2=3.1416 0.707121.5708 S2=π r2=3.1416 0.520.7854  S=S1S2=1.57080.7854=0.785a=1 \ \\ r=a/2=1/2=\dfrac{ 1 }{ 2 }=0.5 \ \\ R=\sqrt{ 2 } \cdot \ a/2=\sqrt{ 2 } \cdot \ 1/2 \doteq 0.7071 \ \\ \ \\ S_{1}=\pi \cdot \ R^2=3.1416 \cdot \ 0.7071^2 \doteq 1.5708 \ \\ S_{2}=\pi \cdot \ r^2=3.1416 \cdot \ 0.5^2 \doteq 0.7854 \ \\ \ \\ S=S_{1}-S_{2}=1.5708-0.7854=0.785



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