In their seminal paper on Euclidean minimum spanning trees, Monma and Suri (1992) proved that any tree of maximum degree 5 admits a planar embedding as a Euclidean minimum spanning tree. Their algorithm constructs embeddings with exponential area; however, the authors conjectured that there exist n-vertex trees of maximum degree 5 that require c(n) x c(n) area to be embedded as Euclidean minimum spanning trees, for some constant c > 1. In this paper, we prove the first exponential lower bound on the area requirements for embedding trees as Euclidean minimum spanning trees.