This question is a bit loosely worded, so some aspects are not completely clear. What follows is my best guess as to what is envisioned by this problem.
It looks like we have a building with one semicircular outer wall into which a door is cut. (Architects would call this the elevation view).
The radius of the semicircle is 6/2 = 3m.
Each point on the edge of semicircle can be described by the coordinate pair (x, sqrt(9 - x2) ) .
The 9 is the square of 3 which is the radius. x is the horizontal distance from the origin. The origin is located in the center at ground level. The y coordinate is the height above ground.
The straight forward approach is to maximize the area = 2x sqrt(9 - x2) with respect to x. Taking the derivative and setting to zero results in x = sqrt(3) and y = sqrt(6). However, sqrt(6) = 2.45. This would lead to 3 - 2.45 vertical clearance from the max height (3) of the wall. This is less than the 1 m required. The conclusion from this is that the constraint ( 1m clearance) is in effect a critical point for the problem.
At this new critical point y =2 (i.e. 3 - the 1 clearance).
So 2 = sqrt(9 -x2) and x = sqrt(5)
The area is 2 x sqrt(9 -x2) = 4 sqrt(5) and the dimensions are
2sqrt(5) by 2.