It is not so regular
In the picture ABEF is a rectangle and BC = CD = DE . What is the ratio between the area of the pentagon CDGHI and the area of the rectangle ABEF ?
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Use coordinate geometry of triangle with BE= 3a, AB=b, and B(0,0) Then we have I(3a/4 , b/4), G(9a/4, b/4), then [ CDGHI] = (3a/2)(b/8) + (5a/2)(b/8) =ab/2 The ratio between the area of the pentagon CDGHI and the area of the rectangle ABEF = 1/6