2 Answers. 0. Balsa trees grow very rapidly (like all pesky trees). Six months after germination, the tree is about 1-1/2 inches in diameter and 10 - 12 feet tall! In 6 to 10 years, the tree is ready for cutting, having reached a height of 60 to 90 feet tall and a diameter of 12 to 45 inches. balsa tree may grow to a diameter of 6 feet or more, but very little usable lumber can be obtained from a tree of this size. The balsa leaf is similar in shape to a grape leaf, only a lot bigger.