Question

An apartment complex has a floor plan with dimensions shown. To effectively air condition a room, 20 BTU’s are required for every square foot. Determine the minimum BTU’s required for an air conditioner to cool the room effectively. Round the answer to the nearest 100 BTU’s.

Answer 1

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 $=\frac{ \pi r^{2} }{2} .$

Here, the diameter is 20 feet so the radius is 10 feet.

The area of the semi-circle $=\frac{ \pi r^{2} }{2} =\frac{ (\pi) (10^{2}) }{2} = 157.079$ square feet.

The area of a rectangle $= (l)(w).$

The length of the rectangle is 22 feet and the width is 20 feet.

The area of a rectangle $= (l)(w) =(22)(20) = 440$ square feet.

The area of a trapezoid $=\frac{a+b}{2} (h).$

Here $a=12, b= 20, h= 3$.

The area of a trapezoid $=\frac{12+20}{2} (3) = 48$ square feet.

Step 3:

The total area of the floor plan $=157.079+440+48 = 645.079$ square feet.

If 20 BTU's are required for a single square foot,

The number of BTU's for 645.079 square feet $= (645.079)(20)=12,901.58$ BTU's.

Rounding this off, we get 12,900 BTU's required  to cool the room effectively.