To find the area of the rectangle, we can use the formula for the area of a rectangle, which is:
\[ \text{Area} = \text{Length} \times \text{Width} \]
The given dimensions of the rectangle are:
-
Length: \(6 \frac{1}{2}\) centimeters, which can be converted to an improper fraction: \[ 6 \frac{1}{2} = 6 + \frac{1}{2} = \frac{12}{2} + \frac{1}{2} = \frac{13}{2} \text{ cm} \]
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Width: \(4 \frac{1}{2}\) centimeters, which can also be converted to an improper fraction: \[ 4 \frac{1}{2} = 4 + \frac{1}{2} = \frac{8}{2} + \frac{1}{2} = \frac{9}{2} \text{ cm} \]
Now, we can calculate the area:
\[ \text{Area} = \left(\frac{13}{2}\right) \times \left(\frac{9}{2}\right) = \frac{13 \times 9}{2 \times 2} = \frac{117}{4} \text{ square centimeters} \]
Now, to convert \(\frac{117}{4}\) into a mixed number:
\[ 117 \div 4 = 29 \quad \text{(remainder 1)} \] Thus, \[ \frac{117}{4} = 29 \frac{1}{4} \text{ square centimeters} \]
Byron calculated the area as 22 square centimeters, which is incorrect. He likely made a mistake by not using the correct dimensions or the method of calculation.
So, the correct choice is:
Byron found the perimeter of the rectangle. The correct area is 29 Start Fraction 1 over 4 End Fraction square centimeters.