The figure is the union of this basic shapes


    - a rectangle 6 x (3+2+2) = 6 x 7 square meters;

    - a semicircle of the diameter (6+(6-2)) = 10 meters (the radius is 10/2 = 5 meters);

    - an isosceles right-angled triangle with the leg size of 3 m;

    - a square of the side length 2 m.



Accordingly, the total area is this sum

      6^7 +  +  +  = 

    = 42 + (1/2)*3.14159*25 + (1/2)*9 + 4 = 89.769875 m^2.


You may round it reasonably and get the


ANSWER.  The total area is  89.77 m^2 rounded with two decimal after the decimal point.