Question

a local business has an area reserved behind the store for a parking lot that is 78 meters long by 19 meters wide. the stalls of the lot are at 90° angles to a required aisle that bisects the lot. the aisle is 8 meters by 78 meters
use the layout of the parking lot to answer the questions.
what is the total area available for cars to park?
$\square\sqrt{}m^{2}$.
if the parking spaces are compact, they have an area of 12.5 $m^{2}$. how many compact parking spaces will fit in the lot?
$\square\sqrt{}$
if the parking spaces are not compact, they will be 3 meters by 5.5 meters. how many noncompact parking spaces will fit in the lot?
$\square\sqrt{}$

Explanation:

Step1: Calculate the total area of the parking - lot

The area of a rectangle is \(A = l\times w\). The total area of the parking - lot \(A_{total}=78\times19\)

$$A_{total}=78\times19=(80 - 2)\times19=80\times19-2\times19=1520 - 38 = 1482\space m^{2}$$

Step2: Calculate the area of the aisle

The area of the aisle \(A_{aisle}=78\times8\)

$$A_{aisle}=78\times8=(80 - 2)\times8=80\times8-2\times8=640 - 16 = 624\space m^{2}$$

Step3: Calculate the area available for parking

The area available for parking \(A = A_{total}-A_{aisle}\)

$$A=1482 - 624=858\space m^{2}$$

Step4: Calculate the number of compact parking spaces

If the area of each compact parking space \(a = 12.5\space m^{2}\), then the number of compact parking spaces \(n_{1}=\frac{A}{a}\)

$$n_{1}=\frac{858}{12.5}=68.64\approx68$$

(we take the integer part since we can't have a fraction of a parking space)

Step5: Calculate the area of a non - compact parking space

The area of a non - compact parking space \(a_{2}=3\times5.5 = 16.5\space m^{2}\)

Step6: Calculate the number of non - compact parking spaces

The number of non - compact parking spaces \(n_{2}=\frac{A}{a_{2}}\)

$$n_{2}=\frac{858}{16.5}=52$$

Answer:

The total area available for cars to park is \(858\space m^{2}\). The number of compact parking spaces is \(68\). The number of non - compact parking spaces is \(52\).