ticks = Table[x, {x, -1, 1, .05}];
g1 = Graphics[Circle[], Frame -> True, ImageSize -> Full,
AspectRatio -> Full,
FrameTicks -> {{ticks, ticks}, {ticks, ticks}}];
g2 = Graphics[Circle[], Frame -> False, ImageSize -> Full,
AspectRatio -> Full];
resizeArea =
Framed@Pane[#, AppearanceElements -> "ResizeArea",
ImageSize -> 100 {1, 1/GoldenRatio}, FrameMargins -> 15] &;
{resizeArea[g1], resizeArea[g2]}