Question

problem | original figure | scale factor | scale drawing | area of the original figure | area of the scale drawing

1. | (1×1 square on grid) | 1/2 | (grid) | |
2. | (1×1 square on grid) | 1/3 | (grid) | |
3. | (2×2 square on grid) | 3 | (grid) | |

Explanation:

Problem 5

Step1: Find original area

The original figure is a square with side length \( s = 1 \). The area of a square is \( A = s^2 \), so original area \( A_{original}=1^2 = 1 \).

Step2: Find scale drawing side length

Scale factor is \( \frac{1}{2} \), so scale drawing side length \( s_{drawing}=1\times\frac{1}{2}=\frac{1}{2} \).

Step3: Find scale drawing area

Area of scale drawing \( A_{drawing}=(\frac{1}{2})^2=\frac{1}{4} \).

Step1: Find original area

Original figure is square with side \( s = 1 \), area \( A_{original}=1^2 = 1 \).

Step2: Find scale drawing side length

Scale factor \( \frac{1}{3} \), so \( s_{drawing}=1\times\frac{1}{3}=\frac{1}{3} \).

Step3: Find scale drawing area

Area \( A_{drawing}=(\frac{1}{3})^2=\frac{1}{9} \).

Step1: Find original area

Original figure is square with side \( s = 2 \), area \( A_{original}=2^2 = 4 \).

Step2: Find scale drawing side length

Scale factor \( 3 \), so \( s_{drawing}=2\times3 = 6 \).

Step3: Find scale drawing area

Area \( A_{drawing}=6^2 = 36 \).

Answer:

Area of Original Figure: \( 1 \), Area of Scale Drawing: \( \frac{1}{4} \)

Problem 6