π is the pi symbol
You can easily find the distance from the center of the square to the corner of the square to be 1/1/
|(We're solving for the shaded regions)|
The method I'm going to use is find the area of one of the shaded regions (top) and multiply that by 4 to get the total area of all 4 regions. We can plot this onto a graph with the center of the circle and square as (0,0). For the circle we have an equation of x^2 + y^2 = 1/3. For the line of the square at the top we have y = 1/2. We can now find the points of intersection of the square and the circle by substituting 1/2 for y.
x^2 + y^2 = 1/3
x^2 + (1/2)^2 = 1/3
x^2 + 1/4 = 1/3
x^2 = 1/4 - 1/3
x^2 = 1/12
x = ±1/
°. That means the angle at the center is also 60° because 180-60-60=60. Now, we can take the area of the part of the circle and subtract the area of the triangle to find the shaded region.
π/3 is the area of the entire circle. However, we only want the area of the 60° slice of the circle. Therefore we multiply the total area by 1/6 because 60° is 1/6 of 360°.
π/3 * 1/6 = π/18
Now we have to subtract the area of the triangle from π/18.