Three Ways to Distort a Shape in Perspective in Adobe Illustrator
First is to use the 3D Rotate effect: Select your shape then go to "Effect > 3D > Rotate...", play with the X, Y & Z axis angles & don't forget to give the Prespective box a value other than 0° ..
Second & maybe the easiest way is the Free Transform tool: Its icon is in the Tools palette on the left & it has "E" as keyboard shortcut. To distort in perspective you have first to select the tool, a frame will surround your selected shape (or shapes), the frame has four handles in the sides & four others in the corners. Start dragging one of the corners handles than do one of the following:
- To distort the shape from the corner you're dragging from, hold "Ctrl" on your keyboard & continue dragging,
- To distort in a symmetric manner, hold the 3 keys "Shift+Ctrl+Alt" & continue dragging.
Once the shape has the form you want, release the mouse button then the keyboard keys (order is important).
Third way is to use one of the Warp effects: (Effect > Warp). The ones I tried are the Arc & Shell effects; both distort in a way that can emulate perspective & also add curves to shapes. Using the Warp effects you can achieve looks impossible using the two other ways.
Note: For the first & third method, if you're about to distort several paths as a unite shape, you should group them together, select the entire group then apply the effect.