I observed that the area of the decagram given on Polytope wiki is not correct: it is higher than the area of the circumcircle. Probably this value has be taken from bendwavy.org where this is not the area but the weighted area which is given (it is defined on this page).
The decagram is a star polygon and it is claimed on Wikipedia that these polygons have been intensively studied. However after googling I have not been able to find a formula for the area of the decagram.
So this question is merely a reference request: where can one find formulas for the area of a star polygon?