Question

Use the image to answer the question.

2 side by side rectangles with the one on the left having sides twice than length of the one on the right.

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 12
. What is the area of the dilated rectangle?

(1 point)
The area of the dilated rectangle is
square inches.
Remaining Attempts : 3

Answer 1

To find the area of the dilated rectangle, we first need to determine the dimensions of the original rectangle and then apply the dilation.

The original rectangle has a height of 6 inches and a base of 8 inches.

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. Since Marc dilates the rectangle using a scale factor of 0.5, we can find the new dimensions:
- New height = \( 6 \times 0.5 = 3 \text{ inches} \)
- New base = \( 8 \times 0.5 = 4 \text{ inches} \)

3. Now 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**.