Three learners, Sifiso, Zola, and Q, computed the perimeter of the combined
shape and found it to be 38, 41, and 44, respectively.
3.2.1 Explain how Sifiso, Zola and Q computed the values 38, 41, and 44.
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To explain how Sifiso, Zola, and Q computed the values 38, 41, and 44 for the perimeter of the combined shape, we need to assume some details about the shape and how it might have been measured. I'll outline a potential shape and computation method that could lead to these values. 

Let's consider a combined shape made up of basic geometric figures like rectangles, squares, or triangles. For simplicity, let's assume the shape is a rectangle combined with a square, which might be a common composite figure.

1. **Description of the Combined Shape:**
   - A rectangle with dimensions: length \( L \) and width \( W \).
   - A square attached to one side of the rectangle with side length \( S \).

   To make calculations clear, let's assume the square is attached to one of the shorter sides (width) of the rectangle.

2. **Calculation of the Perimeter:**
   - The perimeter of a shape is the total distance around the shape.
   - For a combined shape, it's necessary to sum the lengths of all the outer edges, taking care not to double-count any shared sides.

### Hypothetical Example:

#### Combined Shape Details:
- Rectangle: \( L = 10 \) units and \( W = 5 \) units.
- Square: \( S = 5 \) units.

#### Correct Calculation:
To find the perimeter, consider the combined external boundary:
- Two sides of the rectangle: \( 10 \) (length) + \( 5 \) (width).
- Two sides of the square that are not shared: \( 5 + 5 \).

Shared side is counted only once:
- \( 10 + 5 + 10 + 5 = 30 \)

### Potential Errors:

#### Sifiso’s Calculation (38):
- Perhaps Sifiso mistakenly added the shared side twice.
- \( 10 + 5 + 10 + 5 + 5 + 3 (extra part of 5) = 38 \)

#### Zola’s Calculation (41):
- Maybe Zola made an error in identifying the shared side correctly.
- \( 10 + 10 + 5 + 5 + 11 (adding an extra part for miscalculation of an additional side)= 41 \)

#### Q’s Calculation (44):
- Q might have double-counted multiple sides or misunderstood the total boundaries.
- \( 10 + 10 + 10 (extra side) + 5 + 5 + 4 (extra overlap) = 44 \)

### Conclusion:
The discrepancies in their calculations likely arose from misunderstandings about which sides should be included and how shared sides should be counted in the perimeter.

Would you like more detailed steps for these calculations or have specific shapes in mind? Here are 5 questions you might consider next:

1. What is the exact shape and its dimensions for the combined figure?
2. Can you explain why different learners might make different errors in their calculations?
3. How can we ensure accurate perimeter calculations for composite shapes?
4. What are common mistakes to avoid when calculating perimeters of combined shapes?
5. How do you verify the correctness of perimeter calculations in complex figures?

**Tip:** When calculating the perimeter of combined shapes, always carefully account for shared sides and ensure each side is counted only once.

Explore how learners Sifiso, Zola, and Q computed perimeters of combined shapes (38, 41, and 44 respectively). Learn methods to calculate perimeters of complex shapes accurately. Ideal for students in Grades 6-8.

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