Barb is going to cover a rectangular area 8 feet by 10 feet with rectangular paving blocks that are 4 inches by 8 inches by 2 inches to make a flat patio. What is the minimum number of paving blocks she will need if all the paving blocks will face the same direction?
(Note: Barb will not cut any of the paving blocks.)

Options

A. 80
B. 360
C. 601
D. 960

Answer

To find the minimum number of paving blocks needed to cover a rectangular area of 8 feet by 10 feet, we will follow these steps:

### Step 1: Convert the dimensions of the rectangular area from feet to inches.
- The dimensions of the rectangular area are given as 8 feet by 10 feet.
- Since 1 foot equals 12 inches, we convert:
- Length: \( 8 \text{ feet} \times 12 \text{ inches/foot} = 96 \text{ inches} \)
- Width: \( 10 \text{ feet} \times 12 \text{ inches/foot} = 120 \text{ inches} \)

### Step 2: Calculate the area of the rectangular area in square inches.
- The area \( A \) of the rectangle is given by the formula:
\[ A = \text{Length} \times \text{Width} \]
- Substituting the dimensions:
\[ A = 96 \text{ inches} \times 120 \text{ inches} = 11520 \text{ square inches} \]

### Step 3: Calculate the area of one paving block in square inches.
- The dimensions of each paving block are given as 4 inches by 8 inches.
- The area \( A_b \) of one paving block is:
\[ A_b = \text{Length} \times \text{Width} = 4 \text{ inches} \times 8 \text{ inches} = 32 \text{ square inches} \]

### Step 4: Determine the number of paving blocks required.
- To find the number of paving blocks needed, we divide the area of the rectangular area by the area of one paving block:
\[ \text{Number of blocks} = \frac{\text{Area of rectangle}}{\text{Area of one block}} = \frac{11520 \text{ square inches}}{32 \text{ square inches}} = 360 \]

### Conclusion:
- The minimum number of paving blocks Barb will need is **360**.

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