Geometric diagrams e, f, g, and h displaying various shapes with labeled dimensions in millimeters and centimeters.

To solve the problem, we need to calculate the perimeter of each shape shown in the images. The perimeter is the total length of the boundary of a shape. Let's analyze each part step by step.

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Part (e)

The shape consists of two rectangles connected by a small segment. Here are the dimensions:
- Each rectangle has dimensions \(5 \, \text{mm} \times 2 \, \text{mm}\).
- The connecting segment is \(1 \, \text{mm}\) long.

#### Step 1: Perimeter of one rectangle
The perimeter of a single rectangle is given by:
\[
P_{\text{rectangle}} = 2 \times (\text{length} + \text{width}) = 2 \times (5 \, \text{mm} + 2 \, \text{mm}) = 2 \times 7 \, \text{mm} = 14 \, \text{mm}
\]

#### Step 2: Total perimeter of the combined shape
When the two rectangles are connected, the connecting segment reduces the total perimeter because it is counted twice if we simply add the perimeters of the two rectangles. However, since the connecting segment is only \(1 \, \text{mm}\), we need to subtract this overlap from the total perimeter.

The total perimeter without considering the overlap would be:
\[
2 \times 14 \, \text{mm} = 28 \, \text{mm}
\]

Since the connecting segment is \(1 \, \text{mm}\), we subtract this overlap:
\[
P_{\text{total}} = 28 \, \text{mm} - 1 \, \text{mm} = 27 \, \text{mm}
\]

Thus, the perimeter of the shape in part (e) is:
\[
\boxed{27 \, \text{mm}}
\]

---

Part (f)

The shape is a large rectangle with smaller rectangular cutouts on each side. Here are the dimensions:
- The large rectangle has dimensions \(10 \, \text{cm} \times 6 \, \text{cm}\).
- There are four smaller rectangles cut out, each with dimensions \(3 \, \text{cm} \times 2 \, \text{cm}\).

#### Step 1: Perimeter of the large rectangle
The perimeter of the large rectangle is:
\[
P_{\text{large}} = 2 \times (\text{length} + \text{width}) = 2 \times (10 \, \text{cm} + 6 \, \text{cm}) = 2 \times 16 \, \text{cm} = 32 \, \text{cm}
\]

#### Step 2: Perimeter contribution of the cutouts
Each cutout is a rectangle with dimensions \(3 \, \text{cm} \times 2 \, \text{cm}\). The perimeter of one cutout is:
\[
P_{\text{cutout}} = 2 \times (3 \, \text{cm} + 2 \, \text{cm}) = 2 \times 5 \, \text{cm} = 10 \, \text{cm}
\]

Since there are four cutouts, the total perimeter contribution of the cutouts is:
\[
4 \times 10 \, \text{cm} = 40 \, \text{cm}
\]

#### Step 3: Total perimeter of the shape
The total perimeter of the shape is the perimeter of the large rectangle plus the perimeter contributions of the cutouts:
\[
P_{\text{total}} = 32 \, \text{cm} + 40 \, \text{cm} = 72 \, \text{cm}
\]

Thus, the perimeter of the shape in part (f) is:
\[
\boxed{72 \, \text{cm}}
\]

---

Part (g)

The shape is a larger rectangle with a smaller rectangle cut out from the center. Here are the dimensions:
- The larger rectangle has dimensions \(6.4 \, \text{cm} \times 5.8 \, \text{cm}\).
- The smaller rectangle has dimensions \(5.6 \, \text{cm} \times 5.8 \, \text{cm}\).

#### Step 1: Perimeter of the larger rectangle
The perimeter of the larger rectangle is:
\[
P_{\text{larger}} = 2 \times (\text{length} + \text{width}) = 2 \times (6.4 \, \text{cm} + 5.8 \, \text{cm}) = 2 \times 12.2 \, \text{cm} = 24.4 \, \text{cm}
\]

#### Step 2: Perimeter contribution of the cutout
The perimeter of the smaller rectangle is:
\[
P_{\text{smaller}} = 2 \times (\text{length} + \text{width}) = 2 \times (5.6 \, \text{cm} + 5.8 \, \text{cm}) = 2 \times 11.4 \, \text{cm} = 22.8 \, \text{cm}
\]

#### Step 3: Total perimeter of the shape
The total perimeter of the shape is the perimeter of the larger rectangle plus the perimeter of the smaller rectangle:
\[
P_{\text{total}} = 24.4 \, \text{cm} + 22.8 \, \text{cm} = 47.2 \, \text{cm}
\]

Thus, the perimeter of the shape in part (g) is:
\[
\boxed{47.2 \, \text{cm}}
\]

---

Part (h)

The shape is an irregular polygon. We need to sum the lengths of all the sides. Here are the dimensions:
- The sides are labeled as \(3.1 \, \text{cm}\), \(3.4 \, \text{cm}\), \(3.8 \, \text{cm}\), and \(3.7 \, \text{cm}\).

#### Step 1: Sum the lengths of all sides
The perimeter is the sum of all the side lengths:
\[
P_{\text{total}} = 3.1 \, \text{cm} + 3.4 \, \text{cm} + 3.8 \, \text{cm} + 3.7 \, \text{cm}
\]

Perform the addition:
\[
3.1 + 3.4 = 6.5
\]
\[
6.5 + 3.8 = 10.3
\]
\[
10.3 + 3.7 = 14.0
\]

Thus, the perimeter of the shape in part (h) is:
\[
\boxed{14.0 \, \text{cm}}
\]

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Final Answers:

\[
\boxed{27 \, \text{mm}, 72 \, \text{cm}, 47.2 \, \text{cm}, 14.0 \, \text{cm}}
\]