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 12 . 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 calculate the area of the original rectangle and then apply the scale factor.

The area \( A \) of a rectangle is given by the formula:

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

For Marc's 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 scale factor for dilation. The scale factor given is 0.5. When a figure is dilated by a scale factor \( k \), the area of the new figure is given by \( k^2 \) times the area of the original figure.

Calculating the new area after dilation:

\[
\text{New area} = k^2 \times \text{original area} = (0.5)^2 \times 48
\]

Calculating \( (0.5)^2 \):

\[
(0.5)^2 = 0.25
\]

Now, calculate the new area:

\[
\text{New area} = 0.25 \times 48 = 12 \, \text{square inches}
\]

Therefore, the area of the dilated rectangle is:

\[
\text{The area of the dilated rectangle is } 12 \, \text{square inches.}
\]