# Geometry

• May 7th 2008, 09:27 PM
Softballgrl
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
• May 7th 2008, 09:49 PM
Soroban
Hello, Softballgrl!

Quote:

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: . $8^2\:=\:64$ square units.

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

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