Final answer:
The type of stage described in the question is known as a thrust stage, characterized by extending into the audience on three sides, demanding much from the performers and fostering intimate performances.
Step-by-step explanation:
The stage surrounded on three sides by the audience is known as a thrust stage. Unlike a proscenium stage, where the audience faces one side of the stage exclusively, or an arena stage where the audience encircles the performance completely, a thrust stage extends into the audience on three sides. Acting and staging on a thrust stage demand dynamic blocking to ensure performers can be seen from multiple angles, as it limits the traditional 'fourth wall' seen in proscenium theatres.
Thrust stages tend to feature more intimate productions and their design often requires less technical elements. The visibility of technical spaces becomes part of the audience's experience since there is rarely a place to hide the production's workings, unlike the proscenium stage that allows for the complete illusion of a different reality.
In summary, the thrust stage is a popular theatrical space for less technically driven and more intimate performances, offering a closer rapport between the actors and the audience.