Final answer:
The thin filmy tissue surrounding the heart is called the epicardium.
Step-by-step explanation:
The thin filmy tissue surrounding the heart is called the epicardium. It is the outermost layer of the heart wall and is made up of a simple squamous epithelium called a mesothelium. The epicardium is part of the serous pericardium, which consists of two sublayers: the parietal pericardium and the visceral pericardium (epicardium).