Question

Marc draws a rectangle with a height of 6 inches and a base of 8 inches. He dilates the figure using a scale factor of 0.5, or 1/2
. What is the area of the dilated rectangle?

(1 point)
The area of the dilated rectangle is
square inches.

Answer 1

To find the area of the dilated rectangle, we first need to calculate the area of the original rectangle. The area \( A \) of a rectangle is given by the formula:

\[
A = \text{height} \times \text{base}
\]

For the original rectangle:

- Height = 6 inches
- Base = 8 inches

Calculating the area of the original rectangle:

\[
A = 6 \, \text{inches} \times 8 \, \text{inches} = 48 \, \text{square inches}
\]

Next, we apply the dilation. When a shape is dilated by a scale factor of \( k \), the new dimensions become:

- New height = \( 6 \times 0.5 = 3 \) inches
- New base = \( 8 \times 0.5 = 4 \) inches

Now, we calculate the area of the dilated rectangle:

\[
A_{\text{dilated}} = \text{new height} \times \text{new base} = 3 \, \text{inches} \times 4 \, \text{inches} = 12 \, \text{square inches}
\]

Thus, the area of the dilated rectangle is \( \boxed{12} \) square inches.