Question

An image shows a rectangle that is 4 1/2 centimeters tall and 6 1/2 centimeters long.
Byron calculated the area of the rectangle as 22 square centimeters. What is the error in his reasoning and what is the correct answer?

Answer 1

To find the area of a rectangle, you can use the formula:

\[ \text{Area} = \text{length} \times \text{height} \]

In this case, the dimensions given are:
- Height = \( 4 \frac{1}{2} \) centimeters = \( 4.5 \) centimeters
- Length = \( 6 \frac{1}{2} \) centimeters = \( 6.5 \) centimeters

Now, we can calculate the area:

\[
\text{Area} = 4.5 \, \text{cm} \times 6.5 \, \text{cm}
\]

Calculating this step-by-step:

1. Multiply \( 4.5 \) by \( 6.5 \):
\[
4.5 \times 6.5 = 29.25 \, \text{square centimeters}
\]

So the correct area of the rectangle is \( 29.25 \) square centimeters.

Byron's error of calculating the area as \( 22 \) square centimeters may have occurred from a miscalculation or misunderstanding of the multiplication. The correct answer is \( 29.25 \) square centimeters.