CIIM 2021 Problem 1

For every $0 < \alpha < 1$ , let $R(\alpha)$ be the region in $\mathbb{R}^2$ whose boundary is the convex pentagon of vertices $(0,1-\alpha), (\alpha, 0), (1, 0), (1,1)$ and $(0, 1)$ . Let $R$ be the set of points that belong simultaneously to each of the regions $R(\alpha)$ with $0 < \alpha < 1$ , that is, $R =\bigcap_{0<\alpha<1} R(\alpha)$ .

Determine the area of $R$ .