Get path to SQL Server Compact file from Entity Framework context?

I'm trying to programmatically backup my SQL Server CE database. Apparently, this should simply involve copying the database file.

My first solution looked like this:

var connectionString = System.Configuration.ConfigurationManager.ConnectionStrings["MyEntities"].ConnectionString;
var efBuilder = new System.Data.EntityClient.EntityConnectionStringBuilder(connectionString);
var builder = new System.Data.SqlClient.SqlConnectionStringBuilder(efBuilder.ProviderConnectionString);

var src = builder.DataSource.Replace("|DataDirectory|", System.AppDomain.CurrentDomain.BaseDirectory);
var dest = @"C:\temp\backup.sdf";

// file-copy src to dest here

Then it struck me: I'm jumping through hoops here just to duplicate functionality that the Entity Framework is doing internally anyway (not to mention substituting |DataDirectory| with a fixed path).

Then I tried this:

using (var conn = entities.Database.Connection)
{
    // conn.Open();
    var path = conn.Database;
}

where entities is my context but that still only gives me: |DataDirectory|\db.sdf

Question: Is there a proper way to get the actual path to the SQL Server CE file, with |DataDirectory| substituted?

Thanks!