Thread: 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

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: . square units.

The four quarter-circles comprise one circle with radius 4.
. . Its area is: . square units.

Therefore, the shaded region has an area of square units.