Find the area and perimeter of composite figures in this math worksheet.

To solve the problem, we need to calculate the area and perimeter of each composite figure. Let's go through each figure step by step.

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Figure 1:

#### Dimensions:
- Top rectangle: \(10 \, \text{cm} \times 7 \, \text{cm}\)
- Bottom rectangle: \(5 \, \text{cm} \times 4 \, \text{cm}\)

#### Area:
The area of a rectangle is given by:
\[
\text{Area} = \text{length} \times \text{width}
\]

- Area of the top rectangle:
\[
10 \, \text{cm} \times 7 \, \text{cm} = 70 \, \text{cm}^2
\]

- Area of the bottom rectangle:
\[
5 \, \text{cm} \times 4 \, \text{cm} = 20 \, \text{cm}^2
\]

- Total area:
\[
70 \, \text{cm}^2 + 20 \, \text{cm}^2 = 90 \, \text{cm}^2
\]

#### Perimeter:
To find the perimeter, we need to sum the lengths of all the outer edges. The figure can be visualized as a single shape with the following outer dimensions:
- Top side: \(10 \, \text{cm}\)
- Right side: \(7 \, \text{cm} + 4 \, \text{cm} = 11 \, \text{cm}\)
- Bottom side: \(5 \, \text{cm}\)
- Left side: \(3 \, \text{cm} + 7 \, \text{cm} = 10 \, \text{cm}\)

Thus, the perimeter is:
\[
10 \, \text{cm} + 11 \, \text{cm} + 5 \, \text{cm} + 10 \, \text{cm} = 36 \, \text{cm}
\]

#### Answers for Figure 1:
\[
\text{Area} = 90 \, \text{cm}^2, \quad \text{Perimeter} = 36 \, \text{cm}
\]

---

Figure 2:

#### Dimensions:
- Main rectangle: \(10 \, \text{mm} \times 8 \, \text{mm}\)
- Cut-out rectangle: \(6 \, \text{mm} \times 6 \, \text{mm}\)

#### Area:
- Area of the main rectangle:
\[
10 \, \text{mm} \times 8 \, \text{mm} = 80 \, \text{mm}^2
\]

- Area of the cut-out rectangle:
\[
6 \, \text{mm} \times 6 \, \text{mm} = 36 \, \text{mm}^2
\]

- Total area (subtract the cut-out):
\[
80 \, \text{mm}^2 - 36 \, \text{mm}^2 = 44 \, \text{mm}^2
\]

#### Perimeter:
The perimeter of the composite figure is the same as the perimeter of the main rectangle because the cut-out does not affect the outer boundary:
\[
2 \times (10 \, \text{mm} + 8 \, \text{mm}) = 2 \times 18 \, \text{mm} = 36 \, \text{mm}
\]

#### Answers for Figure 2:
\[
\text{Area} = 44 \, \text{mm}^2, \quad \text{Perimeter} = 36 \, \text{mm}
\]

---

Figure 3:

#### Dimensions:
- Top rectangle: \(5 \, \text{m} \times 6 \, \text{m}\)
- Bottom rectangle: \(8 \, \text{m} \times 3 \, \text{m}\)

#### Area:
- Area of the top rectangle:
\[
5 \, \text{m} \times 6 \, \text{m} = 30 \, \text{m}^2
\]

- Area of the bottom rectangle:
\[
8 \, \text{m} \times 3 \, \text{m} = 24 \, \text{m}^2
\]

- Total area:
\[
30 \, \text{m}^2 + 24 \, \text{m}^2 = 54 \, \text{m}^2
\]

#### Perimeter:
To find the perimeter, we sum the lengths of all the outer edges:
- Top side: \(5 \, \text{m}\)
- Right side: \(6 \, \text{m} + 3 \, \text{m} = 9 \, \text{m}\)
- Bottom side: \(8 \, \text{m}\)
- Left side: \(5 \, \text{m} + 8 \, \text{m} = 13 \, \text{m}\)

Thus, the perimeter is:
\[
5 \, \text{m} + 9 \, \text{m} + 8 \, \text{m} + 13 \, \text{m} = 35 \, \text{m}
\]

#### Answers for Figure 3:
\[
\text{Area} = 54 \, \text{m}^2, \quad \text{Perimeter} = 35 \, \text{m}
\]

---

Figure 4:

#### Dimensions:
- Main rectangle: \(8 \, \text{cm} \times 6 \, \text{cm}\)
- Cut-out rectangle: \(4 \, \text{cm} \times 5 \, \text{cm}\)

#### Area:
- Area of the main rectangle:
\[
8 \, \text{cm} \times 6 \, \text{cm} = 48 \, \text{cm}^2
\]

- Area of the cut-out rectangle:
\[
4 \, \text{cm} \times 5 \, \text{cm} = 20 \, \text{cm}^2
\]

- Total area (subtract the cut-out):
\[
48 \, \text{cm}^2 - 20 \, \text{cm}^2 = 28 \, \text{cm}^2
\]

#### Perimeter:
The perimeter of the composite figure is the same as the perimeter of the main rectangle because the cut-out does not affect the outer boundary:
\[
2 \times (8 \, \text{cm} + 6 \, \text{cm}) = 2 \times 14 \, \text{cm} = 28 \, \text{cm}
\]

#### Answers for Figure 4:
\[
\text{Area} = 28 \, \text{cm}^2, \quad \text{Perimeter} = 28 \, \text{cm}
\]

---

Final Answers:

1. \(\text{Area} = 90 \, \text{cm}^2\), \(\text{Perimeter} = 36 \, \text{cm}\)
2. \(\text{Area} = 44 \, \text{mm}^2\), \(\text{Perimeter} = 36 \, \text{mm}\)
3. \(\text{Area} = 54 \, \text{m}^2\), \(\text{Perimeter} = 35 \, \text{m}\)
4. \(\text{Area} = 28 \, \text{cm}^2\), \(\text{Perimeter} = 28 \, \text{cm}\)

\[
\boxed{9036443654352828}
\]