Two area formulas are involved. (You have memorized these, of course.)
Area of a circle:
A = π*r²
where r is the radius
Area of a square:
A = s²
where s is the length of one side
The height and width of the figure are both 4 times the radius of the circle, which is (20 ft)/4 = 5 ft. The side of the square is the diameter of the circle, 10 ft.
The total area is that of 2 full circles of radius 5 ft and one square of side length 10 ft.
.. A = 2*π*(5 ft)² + (10 ft)²
.. = (50π +100) ft²
.. ≈ 257.1 ft²