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To solve this problem, let's break down the information given:

1. The pentagon is **regular**, meaning all its sides are of equal length.
2. The perimeter of the pentagon is **100 mm**.
3. A square is attached to the pentagon.

### Step-by-Step Solution

1. **Find the Side Length of the Pentagon**:
   - Since the pentagon is regular and has a total perimeter of 100 mm, each side of the pentagon is:
     \[
     \frac{100 \, \text{mm}}{5} = 20 \, \text{mm}
     \]

2. **Determine the Side Length of the Square**:
   - The square is attached to one side of the pentagon, so it shares the same side length, which is 20 mm.

3. **Calculate the Perimeter of the Combined Shape**:
   - The combined shape includes the four remaining sides of the pentagon and the three exposed sides of the square.
   - Pentagon sides included in the perimeter: 4 sides \( \times \) 20 mm = 80 mm.
   - Square sides included in the perimeter: 3 sides \( \times \) 20 mm = 60 mm.
   - Total perimeter of the combined shape:
     \[
     80 \, \text{mm} + 60 \, \text{mm} = 140 \, \text{mm}
     \]

### Final Answer
The perimeter of the combined shape is **140 mm**.

Would you like further explanation or have any other questions?

### Related Questions:
1. What is the area of a regular pentagon with a side length of 20 mm?
2. How would the perimeter change if a triangle was attached instead of a square?
3. If the square’s side length was doubled, what would the new perimeter be?
4. What is the perimeter of a hexagon with a side length of 20 mm?
5. How would the perimeter calculation change if the pentagon was irregular?

### Tip:
When dealing with regular polygons, dividing the perimeter by the number of sides gives the side length.

A regular pentagon has a perimeter of 100 mm. A shape is made by joining a square to the pentagon. Work out the perimeter of the shape.

Learn how to calculate the perimeter of a shape formed by attaching a square to a regular pentagon with a 100 mm perimeter. This problem covers geometric concepts and the properties of regular polygons. Suitable for students in Grades 7-9.

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