Frank draws a square that measures 3 inches on each side. Then, he dilates the square using a scale factor of 1.5. What is the area of the dilated square? Use a deicmal response if necessary.

Question

The area of the dilated square is ____ square inches

Answer 1

To find the area of the dilated square, we first need to determine the dimensions of the square after dilation.

1. Original square dimensions: Each side of the original square is 3 inches.

2. Scale factor: The square is dilated using a scale factor of 1.5.

3. New side length: To find the side length of the dilated square, we multiply the original side length by the scale factor:

   \[ \text{New side length} = \text{Original side length} \times \text{Scale factor} = 3 \text{ inches} \times 1.5 = 4.5 \text{ inches} \]

4. Area of the dilated square: The area \(A\) of a square is calculated using the formula:

   \[ A = \text{side length} \times \text{side length} \]

   Substituting the new side length:

   \[ A = 4.5 \text{ inches} \times 4.5 \text{ inches} = 20.25 \text{ square inches} \]

Therefore, the area of the dilated square is 20.25 square inches.