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 compute the area of the original rectangle and then apply the scale factor.

1. Calculate the area of the original rectangle: \[ \text{Area} = \text{height} \times \text{base} = 6 , \text{inches} \times 8 , \text{inches} = 48 , \text{square inches} \]

2. Dilate the dimensions using the scale factor of 0.5:

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

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

Therefore, the area of the dilated rectangle is 12 square inches.