By four groups of equal area which do you mean?
Cut the shape into pieces A, B, C, D and E with the areas
A = B = C = D + E?
or
A = B; A = C + D; B = C + D; C = D + E
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I can get the second scenerio using the edges of the circles as the cut line using circles with the radius of 1, 1, and sqrt(2). The first scenerio...I have no idea yet.