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# Regions Between Circles and Squares

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A common application of the area of a circle and the area of a square are problems where a circle is circumscribed about a square or inscribed in a square. Regions between circles and squares problems almost always involve subtracting the two areas; their difficulty stems from dimensions given for one but not both shapes. Related topics include area of sectors and area of circles.

Once you've learned about the areas of circles and squares it's pretty common that on the test or quiz you're going to be having problems where there's kind of an overlap and you're looking for a shaded region that's in between the circle and the square. So here we have an inscribed circle where we've got 4 points of tangency and all we know is the radius. So we're going to do the general case here, if I asked you for the area of a shaded region. So in your mind you have to think well I'm going to be subtracting a couple of things. And to find the area of the shaded region first I'm going to find the area of the square, so notice I'm not actually saying what that area is I'm just kind of setting up a game plan here. So if I find the area of the square and if I take out the area of the circle then what's left is the shaded region. So I'm going to subtract the area of my circle, so it's always a good place to start off these problems where you have shaded regions with a general game plan and then you can substitute in your formulas.