To determine Byron's error, we need to calculate the area of the rectangle with dimensions 6.5 cm (6 1/2 cm) and 4.5 cm (4 1/2 cm).
The area \( A \) of a rectangle is calculated using the formula:
\[ A = \text{length} \times \text{width} \]
Substituting the values given:
\[ A = 6.5 , \text{cm} \times 4.5 , \text{cm} \]
Calculating this:
\[ A = 6.5 \times 4.5 \]
To perform this multiplication, we can break it down:
\[ 6.5 \times 4.5 = 6.5 \times (4 + 0.5) = 6.5 \times 4 + 6.5 \times 0.5 \]
Calculating each part:
- \( 6.5 \times 4 = 26 \)
- \( 6.5 \times 0.5 = 3.25 \)
Adding these together:
\[ 26 + 3.25 = 29.25 , \text{square centimeters} \]
Thus, the correct area of the rectangle is:
\[ 29.25 , \text{square centimeters} \quad (\text{or} , 29 \frac{1}{4} , \text{square centimeters}) \]
Byron's misunderstanding comes from either miscalculating or misinterpreting the dimensions/events leading to an area of 22 square centimeters. Therefore, the correct answer is:
Byron found the perimeter of the rectangle. The correct area is \(29 \frac{1}{4}\) square centimeters.