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. what is the area of the dilated rectangle.

Answer 1

To find the area of the dilated rectangle, first, we need to determine the dimensions of the rectangle after applying the dilation.

The original rectangle has:
- Height = 6 inches
- Base (width) = 8 inches

The scale factor for the dilation is 0.5. To find the dimensions of the dilated rectangle, we multiply each dimension by the scale factor:

- Dilated height = \( 6 \, \text{inches} \times 0.5 = 3 \, \text{inches} \)
- Dilated base = \( 8 \, \text{inches} \times 0.5 = 4 \, \text{inches} \)

Now, we can calculate the area of the dilated rectangle using the formula for the area of a rectangle:

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

Substituting the dilated dimensions:

\[
\text{Area} = 3 \, \text{inches} \times 4 \, \text{inches} = 12 \, \text{square inches}
\]

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