Odd shower shelf waterproof solution needed

[Donald S.]

Hi everyone,

My new rental has a shower with a weird window ledge. I don't have a picture yet, I'll grab one soon. Basically there's a triangular window ledge, big enough to put 2 dinner plates on. 

The old owner just had wood covered with a piece of plastic. Needless to say, the wood is rotted and using the shower causes leaking.  So how can i fix this? 

I was thinking of using a piece a hardbacker and cover that with red guard waterproof membrane, angling the shelf slightly in towards the shower so water runs back into the shower. Does anyone have a better idea?