Shading under specific total percentage of a density chart

I'm creating a density plot in ggplot2 using geom_density. Is there a way to highlight the first 50% of cumulative density? So in the attached chart (see image) it would shade the left half of the chart until the cumulative density hits 50%.

Or is there a way to calculate the x value at which the cumulative density hits 50%? Thanks for the help!

In general, this is possible. Please provide your code or an example using some toy data and I am sure we can help you.

The general idea would be: calculate the median and, within the ggplot, to split the data into lower and higher groups based on this threshhold.