In the diagram, four circles of radius 4 units intersect at the origin. What is the number of square units in the area of the shaded region? Express your answer in terms of pi.

Thanks!

AnonymousConfusedGuy Apr 18, 2018

#1**+1 **

Look at the diagram, ACG

The area between chord BC and the edge of the top circle can be found as

Area of sector ABC - area of triangle ABC =

(1/4)pi (4)^2 - (1/2)(4^2)sin (90°) =

[ 4pi - 8 ] units^2

And due to symmetry.....we would have 8 of these areas....so....the total area of the shaded regions is

8 ( 4pi - 8 ) =

[ 32 pi - 64] units ^2

CPhill Apr 18, 2018