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Let  the bottom left vertex of the larger squaree= (0,0)

Let the top right vertex of the larger square  = (12,12)

Let the bottom right vertex  of the smaller square  = (18, -6)

One side of the  triangle =  12√2  =   √288 

Another side  of  the  triangle  =  √ (18^2 + 6^2)  = √ (360)   

And the remaining side of the triangle  = √  [ ( 18 -12)^2  + (-6 - 12)^2 ]  = √360  

And the height of this isoceles triangle =  √ [ (√360)^2  - (√72)^2 ]   =  √288

So....the shaded  area  = 

(1/2) (12√2) (√288)  =

6 √2 * √288  =

6 √2 * 12√2  =

144 units^2

Large square side =>   a = 12cm             A = [ b*sqrt(2) + a*sqrt(2) /2] * d/2

---- II ---- diagonal  =>   d

Small square side  =>   b = 6cm                                                 

Green area             =>  A                                               A = 144 cm²