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 :
http://i.imgur.com/oswph.jpg

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.