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The problem involves finding the perimeter of a shape composed of a semicircle and a square, where the arc length of the semicircle is given as 26 cm.

### Step 1: Understanding the components
1. **Semicircle**:
   - The **arc length** of the semicircle is given as 26 cm.
   - The formula for the arc length of a semicircle is:
     \[
     \text{Arc length} = \frac{1}{2} \times 2\pi r = \pi r
     \]
   - Given that \(\text{Arc length} = 26 \, \text{cm}\), we can solve for the radius \(r\):
     \[
     \pi r = 26 \quad \Rightarrow \quad r = \frac{26}{\pi} \approx 8.27 \, \text{cm}
     \]

2. **Square**:
   - The diameter of the semicircle is the same as the side length of the square. Since the radius \(r\) of the semicircle is approximately 8.27 cm, the diameter is:
     \[
     \text{Diameter} = 2r = 2 \times 8.27 = 16.54 \, \text{cm}
     \]
   - Therefore, the side length of the square is 16.54 cm.

### Step 2: Perimeter of the combined shape
The perimeter consists of:
1. The arc of the semicircle (already given as 26 cm).
2. Three sides of the square (since the top side of the square is covered by the diameter of the semicircle). Each side of the square is 16.54 cm.

So, the total perimeter is:
\[
\text{Perimeter} = \text{Arc length} + 3 \times \text{Side length of square}
\]
\[
\text{Perimeter} = 26 + 3 \times 16.54 = 26 + 49.62 = 75.62 \, \text{cm}
\]

### Final Answer:
The perimeter of the shape is **75.6 cm** (rounded to 1 decimal place).

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Do you want more details or have any questions?

Here are 5 related questions:
1. How would the perimeter change if the arc length of the semicircle was different?
2. How do you find the area of the same shape?
3. Can you derive the perimeter formula for any shape combining semicircles and squares?
4. What is the relationship between the radius of a semicircle and its diameter?
5. How do you calculate the perimeter of composite shapes with other curved elements?

**Tip:** Remember that the arc length of a semicircle is \(\pi r\), which helps quickly find the radius when the arc is known.

The shape is made from a semicircle and a square. The length of the arc of the semicircle is 26 cm. Work out the perimeter of the shape. Give your answer in centimeters (cm) to 1 decimal place.

Learn how to calculate the perimeter of a composite shape made from a semicircle and a square, where the arc length of the semicircle is 26 cm. This problem covers geometric concepts and formulas for finding the perimeter, including the relation between the arc length and radius.

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