The 2 triangles shown above are equilateral triangles,
so each sector is 60 degrees.
Hence, the length of the arc is 1/6 of the circumference.
Since there are 6 of such arcs, the parameter formed
by the 6 arcs is equal to the circumference of one circle.
The total parameter of the shaded figure is
8r + circumference -> (8 x 15) + 2 x pi x 15 = 120 + 30pi