Find the area

since the diameter is 2 units ,which is equal to the diagonal of the inscribed square ,so the side of the square is \sqrt{2}.which is equal to the diameter of the smaller semicircles.so the area of the 4 semicircles is 4 (1/2 pi 1/2)=pi.and area of the region inside the circle excluding the square is (pi 1*1)-(\sqrt{2})^2 =pi - 2. therefore area of the shaded region is pi - (pi - 2) = 2 units.

By the Quadrature of the Lune , each shaded area is equal to the area of the triangle it sprouts from. When we draw the square's diagonals, we clearly see these four triangles. Each triangle has an area of $\frac{1}{2}$ , so each lune must have an area of $\frac{1}{2}$ as well. Since there are four lunes, simply multiplying $4 \times \frac{1}{2}$ gets our answer, $2$

since the diameter of the bigger circle is 2 so its radius is 1
and its area is 1 1 pi=pi=3.14
the diameter of the circle is the diagonal of the square
hence the side of the square is √2
so the area of the square is 2.
...the area of the white region outside the square is 1.14.

the diameter of the small circles is equal to √2
and its radius is √2/2.
so the area of the 4 semicircle is equal to the area of two circles with the
same radius and it is equal to
2[(√2/2)^2]*3.14=3.14

after this we are going to subtract the area of the unshaded region which is 1.14
so 3.14-1.14=2

Since, Diameter = 2 Then,Radius = 1 , Then area Circle = Pi Then S.l Square=sqrt(2) , Area Square = 2 |||4 remainingparts area = Pi - 2 |||One remainingpart area = (Pi-2)/4 |||Area each SemiCircle= Pi/4 |||Therefore, Area each shaded part = (Pi/4)-((Pi-2)/4) = 2/4 = 1/2 |||Since we have 4 parts shaded |||Therefore Area of Whole Shaded Part is equal to 0.5 * 4 = 2 (R.t.p) ^^

The area of a shaded area is equal to the area of the smaller semi-circle - the segment of the larger circle defined by a chord which is the diameter of the small circle. Area of semi-circle = (1/2) pi R^2 = (1/2)*pi((sqrt(2)/2)^2 = pi/4. The area of the segment is 1/4 of the area of the large circle - The area of the triangle defined by the 2 radii and the chord = Pi/4 - 1/2. Subtracting, the area of 1 shaded area is 1/2. Multiplying by 4, we get 2. Ed Gray