The radius of circles is √2. Prove that area of non-shaded region is 16+8√3-6π
I can't solve this at all... I can do the three circles area which is 6π, but can't get the rectangular height.
https://i.stack.imgur.com/T5I9E.jpg
Sorry about the picture best I can do on my phone. I'm in a little hurry because my test is tomorrow.
Use the equilateral triangle formed by the centers of the three circles and establish the following relationship between the radius $r$ and the triangle height $h$ using the Pythagorean formula,
$$(2r)^2 = h^2 + r^2$$
which gives $h = \sqrt3 r$. Then, the height of the rectangle is just $h+2r$ and the non-shaded area is $4r(\sqrt3+2)r-3\pi r^2= 16+8\sqrt3-6\pi$.
