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 [tex]=\frac{ \pi r^{2} }{2} .[/tex]
Here, the diameter is 20 feet so the radius is 10 feet.
The area of the semi-circle [tex]=\frac{ \pi r^{2} }{2} =\frac{ (\pi) (10^{2}) }{2} = 157.079[/tex] square feet.
The area of a rectangle [tex]= (l)(w).[/tex]
The length of the rectangle is 22 feet and the width is 20 feet.
The area of a rectangle [tex]= (l)(w) =(22)(20) = 440[/tex] square feet.
The area of a trapezoid [tex]=\frac{a+b}{2} (h).[/tex]
Here [tex]a=12, b= 20, h= 3[/tex].
The area of a trapezoid [tex]=\frac{12+20}{2} (3) = 48[/tex] square feet.
Step 3:
The total area of the floor plan [tex]=157.079+440+48 = 645.079[/tex] square feet.
If 20 BTU's are required for a single square foot,
The number of BTU's for 645.079 square feet [tex]= (645.079)(20)=12,901.58[/tex] BTU's.
Rounding this off, we get 12,900 BTU's required to cool the room effectively.
