A square is inscribed in a circle with diameter 2. Four smaller circles are then constructed with their diameters on each of the sides of the square. Find the shaded area.
+129907 Diagonal of square = 2
Side of square = 2/sqrt (2) = sqrt (2)
Area of white area between the circle and shaded area =
(1/4) (area of circle - area of square) =
(1/4)[ pi (1)^2 - sqrt (2)^2 ] = (1/4) [ pi - 2 ] = ( pi/4 - 1/2 ) (1)
Area of (1/2) circle constructed on the side of the square = (1/2) pi (sqrt (2)/2)^2 = (1/2)pi (2/4) =
(1/2)pi (1/2) = pi/4 (2)
So.....shaded area = (2) - (1) =
pi/4 - (pi/4 - 1/2) =
1/2 units^2
So 4 (1/2) = 2 units^2
