https://file.aiquickdraw.com/mathbot/file/1727277870715jwqkhckt.jpg

I see that you've uploaded a geometry exercise with several problems involving finding the perimeter of various shapes. Let's walk through the problems.

For each shape, the perimeter is calculated by adding up the lengths of all sides. I'll explain the process for each numbered shape:

### 7. Square (3 m x 3 m)
- **Perimeter** = \( 4 \times 3 \, \text{m} = 12 \, \text{m} \)

### 8. Rectangle (11 in x 8 in)
- **Perimeter** = \( 2 \times (11 \, \text{in} + 8 \, \text{in}) = 2 \times 19 \, \text{in} = 38 \, \text{in} \)

### 9. Triangle (sides: 3.9 ft, 5.3 ft, 5.0 ft)
- **Perimeter** = \( 3.9 \, \text{ft} + 5.3 \, \text{ft} + 5.0 \, \text{ft} = 14.2 \, \text{ft} \)

### 10. Trapezoid (sides: 18 in, 23 in, 32 in, 45 in)
- **Perimeter** = \( 18 \, \text{in} + 23 \, \text{in} + 32 \, \text{in} + 45 \, \text{in} = 118 \, \text{in} \)

### 11. Complex Polygon (dimensions: 6 m, 4 m, 2 m, 4 m)
- You have to add all the side lengths. Since it's a symmetrical shape, the total perimeter is:
- **Perimeter** = \( 6 \, \text{m} + 4 \, \text{m} + 2 \, \text{m} + 4 \, \text{m} + 6 \, \text{m} + 4 \, \text{m} = 20 \, \text{m} \)

### 12. Complex Shape (dimensions: 40 in, 12 in, 16 in, etc.)
- The shape has many sides; to calculate the perimeter, you add all the sides:
- **Perimeter** = \( 40 \, \text{in} + 12 \, \text{in} + 12 \, \text{in} + 16 \, \text{in} + 16 \, \text{in} + 12 \, \text{in} = 108 \, \text{in} \)

Do you want more details on any of the shapes or calculations?

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Here are five follow-up questions to expand your understanding:

1. How would the perimeter change for problem 8 if the length increased by 5 inches?
2. What formula is used to find the perimeter of a triangle, given its side lengths?
3. Can you explain why the perimeter of a square is always four times the side length?
4. How do you determine the perimeter of a trapezoid with different side lengths?
5. How does symmetry affect the calculation of the perimeter in problem 11?

**Tip**: Always double-check that you account for all sides when calculating the perimeter, especially for complex shapes!

How do you calculate the perimeter for each of the shapes provided in the image?

Learn how to calculate the perimeter of different shapes, including squares, rectangles, triangles, and trapezoids. This lesson walks through examples and provides detailed explanations for perimeter calculations, suitable for middle school students.

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