Circle Meets Square

Radius is 1 so the area of circle is pi x r^2 = 3.14 x 1^2= 3.14 lets suppose area of square is= y ...... and area of white place is = x ......... then according to the statement the blue and red shaded areas are equal so....... (area of circle) - x= y- x...... 3.14 -x = y - x ..... y-x+x = 3.14 ...... hence the area of Square is y= 3.14

Since the area of the shaded regions of the two shapes are equal, and the un-shaded part where they intersect are also equal, then we can conclude that the area of the circle and the square are equal which is $\pi r^2$ or $\pi (1)^2 = \pi \approx 3.14$

Ar(red region)=ar(green region) [Ar(circle)-ar(white region)]=[ar(square)-ar(white region)] Ar(circle)=ar(square) Ar(square)=π(r^2) r=1

So at(square)=π or 3.1417

If you construct two line segments between the center of the circle and the two vertices, and label the higher vertex A and the lower vertex B, then you find the central angle between the vertices is 90 degrees.

Since the length from the center (h,k) to each vertex is 1, that yields a large 45-45-90 triangle with the small sides being 1 and the hypotenuse being sqrt(2). The area of the white sector is equal to the [(degree of central angle)/360] * r*pi => pi * (1/4) * 1 = pi/4

The area of the entire circle is pi*r^2 = pi(1)^2 = pi The area of the white sector is pi/4 The area of the red part of the circle (and also the area of the blue part of the square) is thus equal to pi-pi/4 = 3pi/4

The problem asks you for the area of the square, which is the area of the sector + area of the blue shaded region = 3pi/4 + pi/4 = pi = ~3.14