Area Of Two Circles With same Radius

[sisxixon]

I know that I should know how to do this problem, but I'm at a loss as to what i should do. Help, please!

A figure is formed with two circles that have the same radius. The radius's length equals the distance between the two centers, which is six. Find the area of the figure.

 

[soroban]

Hello, sisxixon!

A figure is formed with two circles that have the same radius.
The radius's length equals the distance between the two centers, which is six.
Find the area of the figure.

            * * *     * * *
         *         *         *
      *         * / \ *         *
     *         * /   \ *         *
                /     \
    *         */   6   \*         *
    *         * - - - - *         *
    *         *\       /*         *
                \     /
     *         * \   / *         *
      *         * \ / *         *
         *         *         *
            * * *     * * *

I assume we want the area of the entire figure.
This would be the area of the two circles, minus the "overlap".

The figure is filled with equilateral triangles.

The area of the overlap is: \(\displaystyle \text{ two }60^o\text{ sectors, plus two }60^o\text{ segments.}\)
\(\displaystyle \;\;\)I'll let you work it out . . .