Let the diagonal intersection of the square be O, because the triangle BCE is an equilateral triangle with a side length of 1, so its area can be calculated;

Because the EBC angle is equal to 60 degrees and the GBC angle is equal to 45 degrees, the EBG angle is equal to 15 degrees. Because the side length is 1, BO= 2/2. According to the length of BO and the angle EBG equal to 15, the length of BE can be found, and because the angle ABE is equal to 30, the height of triangle with AB as the base can be found. Similarly, the area of triangle CGD can also be calculated.

Finally, subtract the area of triangle Abbe and triangle CGD from the area of square, and then subtract the area of equilateral triangle BEC to get the required area.

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