Annular area

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

Result

S =  0.785

Solution:

$a = 1 \ \\ r = a/2 = 1/2 = \dfrac{ 1 }{ 2 } = 0.5 \ \\ R = \sqrt{ 2 } \cdot \ a/2 = \sqrt{ 2 } \cdot \ 1/2 \doteq 0.7071 \ \\ \ \\ S_{ 1 } = \pi \cdot \ R^2 = 3.1416 \cdot \ 0.7071^2 \doteq 1.5708 \ \\ S_{ 2 } = \pi \cdot \ r^2 = 3.1416 \cdot \ 0.5^2 \doteq 0.7854 \ \\ \ \\ S = S_{ 1 }-S_{ 2 } = 1.5708-0.7854 \doteq 0.7854 = 0.785$

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