Angela uses a scale factor of 1.5 to make a scale drawing of a square. How does the area of the scale drawing compared to that of the original square? Write your answer in decimal form

Answer 1

To find out how the area of the scale drawing compares to that of the original square, we first need to understand how scaling affects area.

1. If the original square has a side length of \( s \), its area \( A \) is calculated as follows: \[ A = s^2. \]

2. When Angela uses a scale factor of 1.5, the side length of the scale drawing becomes: \[ s' = 1.5s. \]

3. The area \( A' \) of the scale drawing can be calculated as follows: \[ A' = (s')^2 = (1.5s)^2. \]

4. Expanding this, we get: \[ A' = 1.5^2 \cdot s^2 = 2.25s^2. \]

5. The area of the original square was \( s^2 \), so now we can compare the area of the scale drawing to the original area: \[ \frac{A'}{A} = \frac{2.25s^2}{s^2} = 2.25. \]

Thus, the area of the scale drawing is 2.25 times the area of the original square. In decimal form, this is: \[ \boxed{2.25}. \]