The first thing to say is that if we define a new random variable $X_i$=$h_ir_i$, then each possible $X_i$,$X_j$ where $i\neq j$, will be independent.
Therefore, we are able to say
Now, since the variance of each $X_i$ will be the same (as they are iid), we are able to say
So now let's pay attention to $X_1$. We know that $h$ and $r$ are independent which allows us to conclude that
(by Fubini's Theorem).
We know that $E(h_1)=0$ and so we can immediately eliminate the second term to give us
And so substituting this back into our desired value gives us
Using the fact that $Var(A)=E(A^2)-E(A)^2$ (and that the expected value of $h_i$ is $0$), we note that for $h_1$ it follows that
And using the same formula for $r_1$, we observe that
Rearranging and substituting into our desired expression, we find that
Note: the other answer provides a broader approach, however, by independence of each $r_i$ with each other, and each $h_i$ with each other, and each $r_i$ with each $h_i$, the problem simplifies down quite a lot.