This very attractive geometrical puzzle is from Catriona Agg. It looks like there isn't enough information, although there is. See the Comments for my solution.
But even after solving it it still feels as though there is an information deficit somewhere!
Here's my take on it.
I arrived at 36 π by minimising the circle so ending up with the horizontal line being the radius of the purple quarter circle. So area = π (12)2 / 4 = 36 π. More of an intuitive solution than a rigorous proof.