### Step-by-Step Solution
Part (a):
Let's start by calculating the areas for both types of parking spaces:
1. Area of the rectangular parking space (Space A):
Given:
- Length of the rectangle = 6 units
- Breadth of the rectangle = 3 units
The area of a rectangle is given by the formula:
[tex]\[
\text{Area of rectangle} = \text{Length} \times \text{Breadth}
\][/tex]
Substitute the given values into the formula:
[tex]\[
\text{Area of rectangle} = 6 \, \text{units} \times 3 \, \text{units} = 18 \, \text{square units}
\][/tex]
2. Area of the parallelogram parking space (Space B):
Given:
- Base of the parallelogram = 4 units
- Height of the parallelogram = 5 units
The area of a parallelogram is given by the formula:
[tex]\[
\text{Area of parallelogram} = \text{Base} \times \text{Height}
\][/tex]
Substitute the given values into the formula:
[tex]\[
\text{Area of parallelogram} = 4 \, \text{units} \times 5 \, \text{units} = 20 \, \text{square units}
\][/tex]
From our calculations:
- Area of the rectangular parking space (Space A) = 18 square units
- Area of the parallelogram parking space (Space B) = 20 square units
Since 20 square units (area of Space B) is greater than 18 square units (area of Space A), the parallelogram parking space (Space B) covers the greater area.
Part (b):
Let's verify our calculations:
1. Re-check the area of the rectangular parking space (Space A):
[tex]\[
\text{Area of rectangle} = 6 \, \text{units} \times 3 \, \text{units} = 18 \, \text{square units}
\][/tex]
2. Re-check the area of the parallelogram parking space (Space B):
[tex]\[
\text{Area of parallelogram} = 4 \, \text{units} \times 5 \, \text{units} = 20 \, \text{square units}
\][/tex]
Given our re-checked and verified calculations:
- The rectangular parking space (Space A) has an area of 18 square units.
- The parallelogram parking space (Space B) has an area of 20 square units.
Therefore, according to both our initial solution and re-checked verification, the parallelogram parking space (Space B) definitively covers the greater area of 20 square units.
