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?

The area of the dilated rectangle is ___square inches

Answer 1

To find the area of the dilated rectangle, we start by calculating the area of the original rectangle.

The area \( A \) of a rectangle can be calculated using the formula:

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

For the original rectangle:

\[
\text{height} = 6 \text{ inches}
\]
\[
\text{base} = 8 \text{ inches}
\]

So the area of the original rectangle is:

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

Next, we apply the dilation using a scale factor of \( 0.5 \). When a rectangle is dilated, both its height and base are multiplied by the scale factor.

Calculating the new dimensions after dilation:

\[
\text{New height} = 6 \times 0.5 = 3 \text{ inches}
\]
\[
\text{New base} = 8 \times 0.5 = 4 \text{ inches}
\]

Now, we calculate the area of the dilated rectangle using its new dimensions:

\[
\text{Area of the dilated rectangle} = \text{new height} \times \text{new base} = 3 \times 4 = 12 \text{ square inches}
\]

Thus, the area of the dilated rectangle is:

\[
\boxed{12} \text{ square inches}
\]