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

Guest Aug 31, 2020

#1**+1 **

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

A_{square} = s^{2}

A_{circle} = πr^{2}

but there are 2 circles so

the total area of the circles is 2πr^{2}

subtract the area of the circles

and what's left is the area of the

shaded region of the square **s ^{2} – 2πr^{2}** and there you have it. Simpler than you thought it would be.

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Guest Aug 31, 2020

#5**+1 **

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