There are at least two artists or groups known as Trapezoid.
1. Trapezoid is an American folk music group. From Wikipedia:

Trapezoid is an American folk music group led by Paul Reisler. Founded in 1975 by Sam Rizzetta, they began as a quartet of hammer dulcimer players. Two of the four played the traditional hammer dulcimer, while the other two played baritone and treble hammer dulcimers specially designed by Rizetta. Since 1975, the group's membership and instrumentation has changed repeatedly, always with Paul Reisler as a member.

In 2004 and 2005, the 1984 lineup that recorded Winter Solstice with John McCutcheon reunited with McCutcheon to perform acoustic concerts, called the Winter Solstice tour. This lineup included fiddler Freyda Epstein, who was killed in 2003 in a car accident.

2. Trapezoid was the musical project of Neil Cicierega before Lemon Demon. A large difference between the two is that a vast majority of Trapezoid's songs were instrumentals, with a few exceptions.

Soon after Neil moved on to Lemon Demon he was contacted by a previously established band by the name of “Trapezoid” (which is most likely the second band on this page), who claimed copyright to the name thus Neil remained the now defunct music project "Deporitaz". Read more on Last.fm. User-contributed text is available under the Creative Commons By-SA License; additional terms may apply.