Question

a maintenance worker needs to wax a restaurant floor shaped like the image shown. if the wax cost $2.25 a square foot, how much will the wax cost to cover the floor? $3,096 $2,106 $1,638 $1,530

Explanation:

Step1: Calculate the area of the triangle

The base of the triangle is \(28 - 16=12\) ft, and the height is \(12\) ft. Using the formula for the area of a triangle \(A=\frac{1}{2}\times base\times height\), we have \(A_1=\frac{1}{2}\times12\times12 = 72\) square - feet.

Step2: Calculate the area of the rectangle

The rectangle has dimensions \(24\) ft (width) and \(12\) ft (height). Using the formula \(A = length\times width\), \(A_2=24\times12 = 288\) square - feet.

Step3: Calculate the area of the other rectangle

The other rectangle has dimensions \(16\) ft (width) and \(32\) ft (height). Using the formula \(A = length\times width\), \(A_3=16\times32=512\) square - feet.

Step4: Calculate the total area

The total area \(A = A_1+A_2+A_3\). So \(A=72 + 288+512=872\) square - feet.

Step5: Calculate the cost

The cost of wax is \(\$2.25\) per square - foot. Using the formula \(C=A\times\) cost per square - foot, \(C = 872\times2.25=\$1962\) (This step - by - step was wrong. Let's correct it.)

Let's re - calculate:

Step1: Calculate the area of the trapezoid - like part (the left - hand side)

The figure can be divided into a triangle and a rectangle.
The base of the triangle \(b = 28 - 16=12\) ft, height \(h = 12\) ft. Area of the triangle \(A_{triangle}=\frac{1}{2}\times12\times12 = 72\) square - feet.
The rectangle adjacent to the triangle has length \(l = 24\) ft and width \(w = 12\) ft. Area of this rectangle \(A_{rect1}=24\times12 = 288\) square - feet.

Step2: Calculate the area of the vertical rectangle

The vertical rectangle has length \(l = 32\) ft and width \(w = 16\) ft. Area \(A_{rect2}=16\times32 = 512\) square - feet.

Step3: Calculate the total area

\(A=72 + 288+512=872\) (wrong). Let's use another decomposition:
The figure can be decomposed into a parallelogram - like part and a rectangle.
The base of the parallelogram - like part (using the formula for the area of a trapezoid \(A=\frac{(a + b)h}{2}\), where \(a = 24\), \(b = 28\), \(h = 12\)) \(A_1=\frac{(24 + 28)\times12}{2}=312\)
The area of the vertical rectangle \(A_2=16\times32 = 512\)
Total area \(A=312+512 = 936\)

Step4: Calculate the cost

The cost \(C=936\times2.25\)

$$
LATEXBLOCK0
$$

Answer:

\(\$2,106\)