Before revision:  We study drawings of trees, outerplanar graphs, and general planar graphs with few segments on a polynomial size grid. For trees , the grid size is n\times n. For 3-connected planar graphs and biconnected outerplanar graphs , we compute such drawings that are also monotone .
After revision:  We study drawings of trees, outerplanar graphs, and general planar graphs with few segments were intensively studied in the past years. However, the area requirements were only considered for limited subclasses of planar graphs. In this paper, we show that trees have drawings with 3n/4-1 segments and n^2 area, improving the previous result of O(n^{3.58 3-connected planar graphs and biconnected outerplanar graphs , we compute such drawings that are also monotone .