  We combine geometric methods with numerical box search algorithm to show that
the minimal area of a convex set on the plane which can cover every closed
plane curve of unit length is at least 0.0975. This improves the best previous
lower bound of 0.096694. In fact, we show that the minimal area of convex hull
of circle, equilateral triangle, and rectangle of perimeter $1$ is between
0.0975 and 0.09763.
