A square piece of paper has side length 1. Esha cuts it in half along one of its diagonals. She labels the corners of one of the triangular halves A. B, C as shown in the left diagram below. Esha folds the triangle so that B is moved to any point B' on the side AC, making a triangle B'GH as shown shaded on the right. H B' B B A a Find the area of AB'GH if B' is at C.

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