It looks to me like the back of the chair is just an arc. To create the same effect in 3D I would draw a narrow, tall rectangle and extrude it along the "path" of the arc. You can use the "slice" command to get the tapered look at each end or you can extrude it just enough so the back of the chair protrudes a "wee bit" into the sides; then use the "union" command to connect it all up. Punch out the horizontal slots with the appropriately shaped wedge and there you have it. Did I miss anything?