Trees are usually drawn planar, i.e. without any crossings. In this paper, we investigate the area requirement of (non-upward) planar straight-line grid drawings of binary trees. Let T be a binary tree with n nodes. We show that T admits a planar straight-line grid drawing with area O(n) and with any pre-specified aspect ratio in the range [1, n ^α ], where α is a constant such that 0 ≤ α < 1. We also show that such a drawing can be constructed in O(n log n) time.