MathDB

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

Problem Statement