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A simple fractal. How to find the area of it? (only the arms of the star)

Working with pentagrams is quite complicated, I can not solve this.

enter image description here

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"Only the arms of the star" mean what? –  GEdgar Nov 4 '12 at 18:08
    
only the external triangles, disregarding the center of the pentagram –  John Smith Nov 4 '12 at 18:16
    
To deal with the infinitely many stars, consider the large pentagon minus the next smaller one, and compute the proportion of that which is covered by arms. As you find that same proportion at every iteration, you can extend it to the whole area of the large pentagon. To compute a single triangle, you either know some numbers that occur in a pentagram, or you go the hard way and start by taking some known angles, and computing coordinates from them using trigonometric functions. –  MvG Nov 5 '12 at 6:09
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