Question

2 1/4 ft (top and bottom), 3 1/5 ft (left and right) (rectangle diagram)

Explanation:

To find the area of the rectangle, we use the formula for the area of a rectangle, \( A = l \times w \), where \( l \) is the length and \( w \) is the width.

Step 1: Convert mixed numbers to improper fractions

• Length \( l = 3\frac{1}{5} \) ft. Converting to an improper fraction:

\( 3\frac{1}{5} = \frac{3 \times 5 + 1}{5} = \frac{16}{5} \)

• Width \( w = 2\frac{1}{4} \) ft. Converting to an improper fraction:

\( 2\frac{1}{4} = \frac{2 \times 4 + 1}{4} = \frac{9}{4} \)

Step 2: Multiply the length and width

Using the formula \( A = l \times w \):
\( A = \frac{16}{5} \times \frac{9}{4} \)

Simplify the multiplication:
\( \frac{16 \times 9}{5 \times 4} = \frac{144}{20} \)

Step 3: Simplify the fraction

Divide numerator and denominator by their greatest common divisor (4):
\( \frac{144 \div 4}{20 \div 4} = \frac{36}{5} \)

Convert back to a mixed number:
\( \frac{36}{5} = 7\frac{1}{5} \)

The area of the rectangle is \( \boldsymbol{7\frac{1}{5}} \) square feet.

Answer:

To find the area of the rectangle, we use the formula for the area of a rectangle, \( A = l \times w \), where \( l \) is the length and \( w \) is the width.

Step 1: Convert mixed numbers to improper fractions

• Length \( l = 3\frac{1}{5} \) ft. Converting to an improper fraction:

\( 3\frac{1}{5} = \frac{3 \times 5 + 1}{5} = \frac{16}{5} \)

• Width \( w = 2\frac{1}{4} \) ft. Converting to an improper fraction:

\( 2\frac{1}{4} = \frac{2 \times 4 + 1}{4} = \frac{9}{4} \)

Step 2: Multiply the length and width

Using the formula \( A = l \times w \):
\( A = \frac{16}{5} \times \frac{9}{4} \)

Simplify the multiplication:
\( \frac{16 \times 9}{5 \times 4} = \frac{144}{20} \)

Step 3: Simplify the fraction

Divide numerator and denominator by their greatest common divisor (4):
\( \frac{144 \div 4}{20 \div 4} = \frac{36}{5} \)

Convert back to a mixed number:
\( \frac{36}{5} = 7\frac{1}{5} \)

The area of the rectangle is \( \boldsymbol{7\frac{1}{5}} \) square feet.