Question

1. complete the table

(table with columns: figure 1, figure 2, figure 3; rows: perimeter (units), area (sq. units); figure 1: perimeter 8, area 3; figure 2: perimeter 16, area 10; figure 3: perimeter 28, area 30)

1. describe any patterns you see.

Explanation:

Question 6: Describe any patterns you see.

To identify patterns, we analyze the Perimeter and Area values for each figure:

• Perimeter: Figure 1 = 8, Figure 2 = 16, Figure 3 = 28. The differences between consecutive perimeters: \( 16 - 8 = 8 \), \( 28 - 16 = 12 \). Wait, maybe another approach. Wait, maybe the figures are related (e.g., growing shapes). Alternatively, check the Area: Figure 1 = 3, Figure 2 = 10, Figure 3 = 30. Wait, maybe the Perimeter and Area both increase as the figure number increases. Let's re-express:
• Perimeter: 8, 16, 28. The increase from Figure 1 to 2: \( 16 - 8 = 8 \); Figure 2 to 3: \( 28 - 16 = 12 \).
• Area: 3, 10, 30. The increase from Figure 1 to 2: \( 10 - 3 = 7 \); Figure 2 to 3: \( 30 - 10 = 20 \). Wait, maybe the figures are composite or follow a linear/quadratic pattern. Alternatively, if we assume the figures are, say, rectangles or other polygons, but the key pattern is that both Perimeter and Area increase as the figure number (1, 2, 3) increases. More precisely, let's check the differences again:
• Perimeter: 8 (Fig1) → 16 (Fig2, +8) → 28 (Fig3, +12).
• Area: 3 (Fig1) → 10 (Fig2, +7) → 30 (Fig3, +20).

Another angle: Maybe the figures are built by adding units, so as the figure grows (higher number), both perimeter (total outer length) and area (total space) increase.

Answer:

As the figure number (1, 2, 3) increases, both the Perimeter (in units) and Area (in square units) increase. Specifically, the Perimeter values are 8, 16, 28 (increasing by 8, then 12), and the Area values are 3, 10, 30 (increasing by 7, then 20), indicating a trend of growth in both measurements as the figure becomes larger or more complex.