The length of a rectangular banner is 3 feet 2 inches, and the width is 2 feet 4 inches. Which one of the following equals the area of the banner?

Options

A. 5 sq. feet
B. 5 1/2 sq. feet
C. 6 1/3 sq. feet
D. 7 7/18 sq. feet

Answer

To find the area of the rectangular banner, we will first convert the dimensions from feet and inches to feet only, then calculate the area using the formula for the area of a rectangle.

### Step-by-Step Solution:

1. **Convert Length from Feet and Inches to Feet:**
- The length of the banner is given as 3 feet 2 inches.
- We know that 1 foot = 12 inches. To convert inches to feet, we divide the number of inches by 12.
- Convert 2 inches to feet:
\[ 2 \text{ inches} = \frac{2}{12} \text{ feet} = \frac{1}{6} \text{ feet} \]
- Now, add this to the feet:
\[ \text{Length} = 3 \text{ feet} + \frac{1}{6} \text{ feet} = \frac{18}{6} + \frac{1}{6} = \frac{19}{6} \text{ feet} \]

2. **Convert Width from Feet and Inches to Feet:**
- The width of the banner is given as 2 feet 4 inches.
- Convert 4 inches to feet:
\[ 4 \text{ inches} = \frac{4}{12} \text{ feet} = \frac{1}{3} \text{ feet} \]
- Now, add this to the feet:
\[ \text{Width} = 2 \text{ feet} + \frac{1}{3} \text{ feet} = \frac{6}{3} + \frac{1}{3} = \frac{7}{3} \text{ feet} \]

3. **Calculate the Area of the Rectangle:**
- The area \( A \) of a rectangle is given by the formula:
\[ A = \text{Length} \times \text{Width} \]
- Substitute the values we found:
\[ A = \left(\frac{19}{6} \text{ feet}\right) \times \left(\frac{7}{3} \text{ feet}\right) \]
- Multiply the fractions:
\[ A = \frac{19 \times 7}{6 \times 3} = \frac{133}{18} \text{ square feet} \]

4. **Convert the Area to Mixed Number:**
- To convert \(\frac{133}{18}\) to a mixed number:
- Divide 133 by 18:
\[ 133 \div 18 = 7 \quad \text{(whole number part)} \]
- Calculate the remainder:
\[ 133 - (18 \times 7) = 133 - 126 = 7 \]
- Thus, the area can be expressed as:
\[ A = 7 \frac{7}{18} \text{ square feet} \]

### Final Answer:
The area of the banner is \( 7 \frac{7}{18} \) square feet.

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