MathDB

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Part of 2021 CIIM

Problems(1)

Calculate the overlapping area

Source: 2021 CIIM, P1

11/2/2021
For every 0<α<10 < \alpha < 1, let R(α)R(\alpha) be the region in R2\mathbb{R}^2 whose boundary is the convex pentagon of vertices (0,1−α),(α,0),(1,0),(1,1)(0,1-\alpha), (\alpha, 0), (1, 0), (1,1) and (0,1)(0, 1). Let RR be the set of points that belong simultaneously to each of the regions R(α)R(\alpha) with 0<α<10 < \alpha < 1, that is, R=⋂0<α<1R(α)R =\bigcap_{0<\alpha<1} R(\alpha).
Determine the area of RR.
calculusanalytic geometrygeometry