1. ## Geometry

Hi,
Okay i am stuck on this problem. There is a square with four congruent quarter circles in it, each with a radius of four. In the middle of the square there is a shaded region that resembles a curved diamond shape, which i am supposed to find the area of.

Thanks for any help

2. Hello, Softballgrl!

There is a square with four congruent quarter circles in it,
each with a radius of four. In the middle of the square there is a shaded region
that resembles a curved diamond shape, which i am supposed to find the area of.
Code:
           4         4
* - - - - * - - - - *
|         *         |
|         :         |
4 |        *:*        |
|       *:::*       |
|     *:::::::*     |
* *:::::::::::::::* * 8
|     *:::::::*     |
|       *:::*       |
4 |        *:*        |
|         :         |
|         *         |
* - - - - * - - - - *
8

The square has an area of: .$\displaystyle 8^2\:=\:64$ square units.

The four quarter-circles comprise one circle with radius 4.
. . Its area is: .$\displaystyle \pi r^2\:=\:16\pi$ square units.

Therefore, the shaded region has an area of $\displaystyle (64 - 16\pi)$ square units.