Friedrich Engemann was hired as a teacher of architectural drawing, construction and descriptive geometry at the Bauhaus. He temporarily took over direction of the building and interior design department as the deputy to Ludwig Mies van der Rohe.
The brother of Bauhausler Herbert Engemann, Friedrich initially completed his training to become a mason, then attended the Polytechnic Institute for Civil Engineering in Gorlitz and had his first professional experience at the Hentschel architecture office. In 1923, he enrolled for one year at the Trade Academy in Chemnitz and was hired that same year as a technical schoolmaster at the Commercial Vocational School of Gorlitz. After an additional apprenticeship as a cabinetmaker, Friedrich Engemann began his studies of interior design and art criticism at the Applied Arts Academy in Dresden. In 1925, he married the weaver Alma Else Imboden and she later also came to the Bauhaus Dessau as a guest auditor. In 1927, his path led him to Dessau, where he taught at the trade vocational and professional schools until 1933. At the same time, he was at the Bauhaus in Dessau and Berlin - first as a student, then later as a teacher.
At the Bauhaus Dessau initially attended the preliminary course with Josef Albers and took classes with Wassily Kandinsky, Paul Klee and Joost Schmidt. He was subsequently hired as a teacher for architectural drawing, construction and descriptive geometry, the last level of the three-level training at the Bauhaus. In 1933, Engemann joined the NSDAP and became the director of the wood department at the Technical Institute in Dessau until 1939. During the Second World War, he designed and constructed air defence and aircraft reporting schools.
Together with the former Bauhausler Hubert Hoffmann, he actively promoted the revival of the Bauhaus after the end of the war. During the GDR era, Engemann held numerous public offices such as the Chairman of the Council for Industrial Form at the Ministry for Culture. Starting in 1948, he also worked at the Institute for Artistic Work Design in Halle/Saale, Burg Giebichenstein. This was later renamed as the University for Industrial Form Design of Halle - Burg Giebichenstein. Ten years later, he was appointed as its vice-chancellor for research and education.