Calculate the surface area of the part of the sphere x^2 + y^2 + z^2 = 1 that is contained in the lemniscata (x^2 + y^2)^2 = x^2 - y^2

I solved this quickly but i cant seem to get the same answer given in the book, And i would like to know which is the correct one. thanks in advance to anyone that helps.(Clapping)