Question

math pie

Answer 1

the square and circle have the same center. the circle has a radius of r. what is the area of the shaded region

Answer 2

dont judge the drawing i tried

Answer 3

@Pixel

Answer 4

So essentially you have a circle inscribed in a square, and you are asked to find the area bounded outside the circle but within the square:



You can find that by subtracting the area of the circle from the area of the square, correct?

Area of square - Area of circle = area of shaded region

Now we must find expressions for each

Area of square:


If you notice, doubling the radius gives you the diameter, which should be equivalent to a side length of a square. We get that as 2r
Hence, the area of the square is (2r)^2 = 4r^2

Area of the circle is easy, pi * r^2

Hence, the area of the shaded region is

\(A=4r^2 - \pi r^2\)