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# geometry

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How to find the area of a square (shaded in) with two circles. I need to find how to get the area. Aug 31, 2020

#1
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You would subtract the two circles' area from the square's area.

Asquare  =  s2

Acircle     =  πr2

but there are 2 circles so

the total area of the circles is                  2πr2

subtract the area of the circles

and what's left is the area of the

shaded region of the square                 s2 – 2πr2     and there you have it.  Simpler than you thought it would be.

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Aug 31, 2020
#2
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That is true but it can be written in terms of just s or just r.

Melody  Aug 31, 2020
edited by Melody  Aug 31, 2020
#5
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You can draw the perpendiculars from the center of a circle to the nearest sides of the square.  Then the length of that small square's diagonal would be the radius times the square root of two.  Do the same with the other circle, then add those two diagonals and the two radii between them, and that gives you the diagonal of the large square in terms of r.  Divide that by the square root of two and you have the side of the square in terms of r.

Then you can express the area of the square in terms of r and the area of the circles in terms of r, and subtract the latter from the former.

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Guest Aug 31, 2020
#3
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The question should be: what is the ratio of the area of the shaded region to the area of both circles?

Aug 31, 2020
#4
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You can work out the diagonal in terms of s

and as a separate issue you can work it out in terms of r.

Then you can put them equal to each other to get r in terms of s   OR s in terms of r

Aug 31, 2020