12,900 BTU's are required to cool the room effectively.
Step-by-step explanation:
Step 1:
We must calculate the area of the entire shape to determine the minimum BTU's required to cool the room effectively.
It is made up of a semi-circle a rectangle, and a trapezoid.
Step 2:
The area of a semi-circle 
Here, the diameter is 20 feet so the radius is 10 feet.
The area of the semi-circle
square feet.
The area of a rectangle 
The length of the rectangle is 22 feet and the width is 20 feet.
The area of a rectangle
square feet.
The area of a trapezoid 
Here
.
The area of a trapezoid
square feet.
Step 3:
The total area of the floor plan
square feet.
If 20 BTU's are required for a single square foot,
The number of BTU's for 645.079 square feet
BTU's.
Rounding this off, we get 12,900 BTU's required to cool the room effectively.