The area directly behind the net marked by red lines where the goaltender is allowed to play the puck below the goal line. A minor penalty is assessed to a goalie who plays the puck below the goal line outside the trapezoid.
It wasn't until the 2005-2006 season coming out of the National Hockey League - NHL's lost season and lockout that the trapezoid was painted in arenas.
This was an attempt to reduce goaltenders, specifically good puck-handling ones such as Martin Brodeur and Marty Turco, from becoming a third defenseman who couldn't be body checked. The goalies could pretty much take away any dump-in to the corners and easily clear the puck to a teammate.
The introduction and enforcement of the trapezoid and its intended use to help create more offensive chances has been contested greatly. Critiques argue it has taken a skill away from some top-end netminders. Other argue it hasn't helped offense the way it was thought it could. Goalies now stop the puck if possible before it reaches the corner in order to move the puck like the old days.
Many other leagues at the amateur and pro levels around the world do not enforce the trapezoid rule. Changes to the this rule are discussed often and could be seen in the near future.