Question

7.1.01
problems 5–6: figures 1, 2, and 3 are scaled copies of each other. each small square has a side length of 1 unit and an area of 1 square unit.

1. complete the table.

\t\t\tfigure 1\tfigure 2\tfigure 3
perimeter (units)\t8\t\t\t
area (sq. units)\t3\t\t\t

Explanation:

Step1: Analyze Scaling Factor

Since Figure 2 and Figure 3 are scaled copies of Figure 1, we first find the scaling factor. By comparing the side lengths (number of small squares along a side), Figure 2 seems to have a scaling factor of 2 (each dimension is doubled), and Figure 3 has a scaling factor of 3 (each dimension is tripled) relative to Figure 1.

Step2: Calculate Perimeter for Figure 2

For similar figures, perimeter scales with the scaling factor. Figure 1 has a perimeter of 8. Scaling factor for Figure 2 is 2, so perimeter of Figure 2 = \( 8 \times 2 = 16 \).

Step3: Calculate Perimeter for Figure 3

Scaling factor for Figure 3 is 3, so perimeter of Figure 3 = \( 8 \times 3 = 24 \).

Step4: Calculate Area for Figure 2

For similar figures, area scales with the square of the scaling factor. Figure 1 has an area of 3. Scaling factor for Figure 2 is 2, so area of Figure 2 = \( 3 \times 2^2 = 3 \times 4 = 12 \).

Step5: Calculate Area for Figure 3

Scaling factor for Figure 3 is 3, so area of Figure 3 = \( 3 \times 3^2 = 3 \times 9 = 27 \).

Answer:

	Figure 1	Figure 2	Figure 3
Area (sq. units)	3	12	27

(For the table completion, the values for Figure 2 Perimeter: 16, Figure 2 Area: 12, Figure 3 Perimeter: 24, Figure 3 Area: 27)