I have tried solving this question by first finding the Area of circle and then area of square (via diagonal method). and then subtracted Its value from the total area But my answer is coming $16\pi – 20.$ But the given options are $4\pi + 1 ,\, 4\pi – 1,\,4\pi – 2,$ none. I'm badly stuck. Kindly tell me the correct answer along the some explanation. Thanks.
Here are the steps I took, In details.
1) First I calculate the Area of the circle through radius, which is A = 16π.
2) Then I calculate the area of the square through this method:
" A square is also a rhombus (with equal diagonals), so we can use the formula for the area of the rhombus. What do we use as the value of the diagonal? The diameter of the circle! "
Area of square here = 32
Dividing sq. into half = 16 + not shaded region of other half 4 == 20
So the total shaded Area becomes 16π – 20.
Where Am I wrong? Kindly explain.
Best Answer
As noted in the comments, there are four separate parts of the circle outside the square, and it appears that only one of those four parts is shaded. Assuming this is correct (which appears to be true), you are correct that the single outside shaded region has area $4\pi - 8$ and the inside region (the shaded quadrilateral within the square) has area $12.$
So we agree that the total is $4\pi + 4,$ which means only the "none of these" answer can be correct.