Compute $E(X\mid X> \frac{a}{1+Y} ) $ if $(X,Y)$ is uniformly distributed on a triangle

Question

Consider the joint uniform distribution $f(x,y) = 1$ on the triangle defined by the inequations $0<x<1$, $0<y<2$, $\frac12y+x\leq 1$.

Compute $E(X\mid X> \frac{a}{1+Y} ) $ for a given $a$.

I know how to evaluate conditional expectations, but I'm confused about how to evaluate it when $X$ depends on $Y$ and $Y$ is part of the condition.