The area of the white square is 64 square units. The diagonal of the square was extended to point A until the length of segment AB was double the length of the diagonal of the square. What is the area of the gray part?

Area of the gray region = 64 square units

Step-by-step explanation:

Area of the white square = 64 square units

Length of a side of the given square =

                                                             =

                                                             = 8 units

By Pythagoras theorem,

Length of diagonal DB =

DB =

     =

AD = DB = [Given]

OD = OC =

               = 4√2

Therefore, AO = AD + OD = 8√2 + 4√2

                                           = 12√2

Area of ΔACD = Area of ΔAOC - Area of ΔCOD

                        =

                        =

                        =

                        = 32

Therefore, area of gray part = Area of ΔACD + Area of ΔAED

                                               = 32 + 32

                                               = 64 square units

64 square units

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step-by-step explanation: vsfdvsfvd