Find the total area of the shaded area in the figure if all circles have an equal radius $R$ and the centers of the outer circles divide into six equal parts of the middle circle.
[img]http://3.bp.blogspot.com/-Ax0QJ38poYU/XovXkdaM-3I/AAAAAAAALvM/DAZGVV7TQjEnSf2y1mbnse8lL6YIg-BQgCK4BGAYYCw/s400/estonia%2B2000%2Bo.j.1.5.png[/img]
To find the total area of the shaded region, we need to calculate the area of one petal and then multiply it by 6, as there are 6 petals in the figure.

1. **Calculate the area of the equilateral triangle:**
   Each petal can be divided into an equilateral triangle and two segments of a circle. The side length of the equilateral triangle is equal to the radius \( R \) of the circles.
   \[
   \text{Area of the equilateral triangle} = \frac{R^2 \sqrt{3}}{4}
   \]

2. **Calculate the area of the sector:**
   The sector of the circle has an angle of \( \frac{\pi}{3} \) radians (60 degrees).
   \[
   \text{Area of the sector} = \frac{\pi R^2}{6}
   \]

3. **Calculate the area of the segment:**
   The segment is the area of the sector minus the area of the equilateral triangle.
   \[
   \text{Area of the segment} = \frac{\pi R^2}{6} - \frac{R^2 \sqrt{3}}{4}
   \]

4. **Calculate the area of one petal:**
   Each petal consists of two segments.
   \[
   \text{Area of one petal} = 2 \left( \frac{\pi R^2}{6} - \frac{R^2 \sqrt{3}}{4} \right)
   \]

5. **Calculate the total area of the shaded region:**
   There are 6 petals in total.
   \[
   \text{Total area of the shaded region} = 6 \times \left( 2 \left( \frac{\pi R^2}{6} - \frac{R^2 \sqrt{3}}{4} \right) \right)
   \]
   Simplify the expression:
   \[
   \text{Total area of the shaded region} = 12 \left( \frac{\pi R^2}{6} - \frac{R^2 \sqrt{3}}{4} \right)
   \]
   \[
   \text{Total area of the shaded region} = 2 \pi R^2 - 3 R^2 \sqrt{3}
   \]

The final answer is \(\boxed{2 \pi R^2 - 3 R^2 \sqrt{3}}\)