Day 4: Cutting out Decorations

Geometry Level 2

A mathematician is cutting out an interesting star shape to use as a Christmas tree decoration. She cuts it out of a rhombus shaped card, and the rhombus has side-length 8. The star is made by cutting off circular sectors centered at each vertex that touch at the midpoints of the sides (as shown in the diagram above).

Find the perimeter of the star.


This problem is part of the Advent Calendar 2015.
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