  The visual complexity of a graph drawing can be measured by the number of
geometric objects used for the representation of its elements. In this paper,
we study planar graph drawings where edges are represented by few segments. In
such a drawing, one segment may represent multiple edges forming a path.
Drawings of 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
$O(n^{3.58})$. We also show that 3-connected planar graphs and biconnected
outerplanar graphs have a drawing with $8n/3-O(1)$ and $3n/2-O(1)$ segments,
respectively, and $O(n^3)$ area.
