Find the area of the black region

A doctor of psychology was doing his normal morning rounds, and he entered a patient's room to find his patient sitting on the floor, sawing at a piece of wood with the side of his hand. Meanwhile, another patient was in the room, hanging from the ceiling by his feet.The doctor asked his patient what he was doing, sitting on the floor.
The patient replied in an irritated fashion, "Can't you see I'm sawing this piece of wood in half?"
The doctor inquired, "And what is the fellow hanging from the ceiling doing?"
"Oh. He's my friend, but he's a little crazy. He thinks he's a light bulb."
The doctor asks, "If he's your friend, don't you think you should get him down from there before he hurts himself?"
"What? And work in the dark?"