Modelling a table mat

Hello everyone. Simple modelling question.
I am trying to model this mat:

As you can see, it’s got a circle shape near the bottom right corner.
How would i go about modelling that?

I have tried this method:

Start with a plane, delete the bottom-right vertice, add a circle while in edit mode, delete the verts i don’t need, merge vertices.

Then i end up with this:

After that, i extrude it so i end up with this:

My question is: how do i cap this so it’s solid?

I selected the top edge loop, extruded, hit escape, and merge at centre.
I did the same for the bottom edge loop.

Any better solutions you recommend?

This is the result i got:

Can anyone recommend a better solution?

Maybe try like this :

It should be less faces, and does not need an additional vertice near the rounded part.

If you are in blender 2.5 just select one loop at time and press ALT+F (Beauty fill)

This is what i get with beauty fill:

Either way, i get a clean render of this object.

Thanks for all your suggestions!

Here’s a render of my scene with the table mat.

Why you didn’t use a Bezier Curve for simple shape like this?

Well Robsoie is the best method, however I recommend to add another loopcut (Ctrl+R) on the large (partly) hexagonal square to increase the value of the mesh.