Question

Which has the greater area: a 6
‐centimeter by 412
‐centimeter rectangle or a square with a side that measures 5
centimeters?

Answer 1

To find the area of each shape, we can use the formulas for area:

1. **Rectangle**: The area \( A \) of a rectangle is given by the formula:
\[
A = \text{length} \times \text{width}
\]

For the rectangle with dimensions 6 cm by 412 cm:
\[
A_{\text{rectangle}} = 6 \, \text{cm} \times 412 \, \text{cm} = 2472 \, \text{cm}^2
\]

2. **Square**: The area \( A \) of a square is given by the formula:
\[
A = \text{side}^2
\]

For the square with a side of 5 cm:
\[
A_{\text{square}} = 5 \, \text{cm} \times 5 \, \text{cm} = 25 \, \text{cm}^2
\]

Now we can compare the two areas:
- Area of the rectangle: \( 2472 \, \text{cm}^2 \)
- Area of the square: \( 25 \, \text{cm}^2 \)

Thus, the rectangle has the greater area.