How to make a kid understand geometry and help him solve problems? I'm tutoring a 13 year-old boy, a middle school student.
He has almost no problem with elementary algebra: he just applies the rules and everything falls into place. However he does struggle with geometry, since straight applying rules isn't always enough.
The more complex the problem, the less he's able to find a path to the solution.
I'll give an example. We encountered a problem like this one:

Where the goal is to find the area of the shaded region. He was able to find the area of circular sector and triangle, but he could not put the pieces together without my help.
I don't want to suggest a solving path every time, because I'd like to improve his ability of finding one on his own.
So, here's my question: what should I do in order to improve his problem-solving skills, especially when he needs to use some creativity to reach the solution?
 A: Since he's good at algebra, you could suggest he try to apply it in geometry when he gets stuck. I don't mean it'll be a feasible method on its own for all geometry; traditional Euclidean methods are often more productive than writing everything in Cartesian coordinates. However, consider your problem example. We want to compute a sum of two grey areas $g_1+g_2$, given that the white areas $w_1,\,w_2$ satisfy $g_1+w_1=g_2+w_2=32$ and $g_1+w_1+g_2=16\pi$.
I realise people at our level effectively think through the problem that way anyway, but your student might not have realised he can do that. Some students are excellent at juggling facts about letters' unknown values, but not so good (until better instructed) at applying this to specific meanings for those letters. In other words, they could solve the equations I just wrote, but wouldn't spot they're lurking in the diagram. I once knew a maths teacher who told me he'd encountered students who knew how to solve $ax^2+bx+c=0$, but not $at^2+bt+c=0$. I kid you not!
