Born in Järsi village, at the time part of Järva County, on July 23, 1929, Areng began his music studies in Rakvere, where he studied piano in a newly opened children's music school and took private lessons with Glafira Roi.

After graduating high school, Areng entered into military service on the Black Sea coast, and graduated with a degree in piano from Sukhumi Music School. In 1959, he graduated from Tallinn State Conservatory with a degree in choir direction under professor Gustav Ernesaks, and in 1965 completed an assistenture at Leningrad Conservatory under the direction of Yelizaveta Kudryavtsev.

Best known over his career for his consistent work in choir direction, Areng was also a prolific pedagogue, helping educate in turn a long line of recognized Estonian choir directors and conductors, including Anne Dorbek, Toomas Kapten, Elo Forsel (Üleoja), Laine Jänes, Indrek Vijard, Olari Elts, Lauri Sirp, Risto Joost, Peeter Perens, Jr., Triin Koch, Veronika Portsmuth, among others.

Areng began working as a teacher at the Estonian Academy of Music and Theatre in 1962, where he earned the status of professor in 1982 and served as director of the Choir Direction Department from 1985-1992. In 2003, he earned the title of professor emeritus.

A number of Estonia's more prestigious choirs were under Areng's direction for decades. From 1966-1990, Areng worked as conductor for the Estonian National Male Choir (RAM), during which time he conducted concerts in a number of countries abroad, including Germany, Finland, Sweden, Italy and the U.S., and performed in the world's most prestigious concert halls, including the Moscow Conservatory, the Grand Hall of the St. Petersburg Philharmonia, the John F. Kennedy Center for the Performing Arts in Washington, and New York's Carnegie Hall.

Areng also directed the State Choir Directors' Mixed Choir from 1961-2000, the Estonian Male Song Society's Tallinn Men's Choir beginning in 1989, and was chief conductor of the Estonian Academy of Sciences Men's Choir. From 1962-1993, he also directed the Tallinn Chamber Choir, from 1978-1993 as chief conductor, and thereafter as honorary conductor. Beginning in 1965, Areng had likewise repeatedly been chief director of the national song festival.

Among other prizes and awards, Areng was bestowed the Order of the White Star, 3rd Class in 2000, a Cultural Award of the Republic of Estonia in 2003, and the Estonian National Culture Foundation's Lifetime Achievement Award in 2009. In 2014, he also earned a Town Hall Medal from the city of Tallinn for his longtime outstanding work as a conductor and teacher.