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Find the area of then polygon

92.75 cm^2

Step-by-step explanation:

Area of triangle ADC

= (1/2)×4.5×12 = 27

Area of triangle ACB

=(1/2)×12×5 = 30

Find AB using pythagoras theorem on triangle ABC:

AB^2 = 5^2 + 12^2 = 25 + 144

AB^2 = 169

AB = 13cm

Area of triangle AGB

= (1/2)×13×5.5 = 35.75

Total area = sum of the areas of the 3 triangles found above

= 27 + 30 + 35.75 = 92.75 cm^2