Question

Marc draws a rectangle with a height of 6 inches and 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?

Answer 1

To find the area of the dilated rectangle, we first need to calculate the dimensions of the original rectangle and then apply the scale factor to get the new dimensions.

The original dimensions are:
- Height = 6 inches
- Base = 8 inches

The area of the original rectangle is given by the formula for the area of a rectangle:

\[
\text{Area} = \text{Height} \times \text{Base}
\]

Calculating the area of the original rectangle:

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

Now, Marc dilates the rectangle using a scale factor of \(0.5\). To find the new dimensions, we multiply each dimension by the scale factor:

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

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

\[
\text{Area of dilated rectangle} = \text{New Height} \times \text{New Base}
\]

Calculating the area of the dilated rectangle:

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

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