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?

Question

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:

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