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 first need to determine the dimensions of the rectangle after dilation.

The original rectangle has a height of 6 inches and a base of 8 inches. When we apply a scale factor of 0.5 (or 1/2), we multiply both the height and the base by this scale factor:

1. New height:
   \[ \text{New height} = \text{Original height} \times \text{Scale factor} = 6 \text{ inches} \times 0.5 = 3 \text{ inches} \]

2. New base:
   \[ \text{New base} = \text{Original base} \times \text{Scale factor} = 8 \text{ inches} \times 0.5 = 4 \text{ inches} \]

Now, we can calculate the area of the dilated rectangle. The area \( A \) of a rectangle is given by the formula:

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

Substituting the new dimensions into the formula:

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

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