Triangle P has vertices at A (0,0), B (1, 1) and C (2,0).

Triangle Q is isosceles, with vertices at D (0, 2k), E (k, 0) and F(2k, 2k), where   0 < k < 2.

The shape formed by the overlap of P and Q is called R.

For what value(s) of k is the area of R equal to exactly one-sixth of a square unit?