# Shaded Area under square inscribed in a Circle.

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.

• Work through the problem step by step, writing down what you have done at every step. If you are still not confident in your answer (indeed, what you wrote seems obviously too large), then you can copy your work (all of it!) into the question so that someone may be able to find your error and put you on the right track. – David K Nov 14 '18 at 13:58
• I just added the proper screenshot check this one please. – shawn k Nov 14 '18 at 14:01
• @DavidK I just edited my question, Kindly check. – shawn k Nov 14 '18 at 14:12
• Only the left segment of the circle is shaded, the other three are not. The area you calculated still includes all four of those segments. (You took the circle and subtracted the unshaded areas inside the square.) Try calculating the two shaded parts separately. – Jaap Scherphuis Nov 14 '18 at 16:25
• @JaapScherphuis Thank you so much for the hint. So according to that that one shaded region outside is of 4π - 8, so adding both will be 4π - 8 + 12(inside region) = 4π + 4. Is that Correct? So the final answer from the options will be none? – shawn k Nov 14 '18 at 17:23

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.

• Note that this answer is merely a summary of some of the comments so that you can decide whether your question is answered. I don't get any credit if you accept this answer, but after you have had some time to consider it (and other people have had a chance to post a better answer if they have one), accepting this answer would let people know you have gotten what you need. – David K Nov 14 '18 at 20:06
• Ok. Just did it. – shawn k Nov 17 '18 at 8:16