The umbrella shaped fruiting body of a fully developed mushroom is the

The umbrella-shaped fruiting body of a fully developed mushroom is called the Pileus. The Pileus is the cap or top part of the mushroom that contains the spore-bearing structures underneath. It is usually broad and flat or convex, and can vary in color, shape, and texture depending on the species of the mushroom. The Pileus is an important part of the mushroom's reproductive system, as it is responsible for producing and releasing spores that can give rise to new mushroom colonies. The spores are produced on the gills, which are located on the underside of the Pileus. When the spores are mature, they are released into the air and can be dispersed by wind or other means. Therefore, the correct answer is option A: Pileus.