Area and Perimeter Sheet 4 - Calculate missing sides and find area and perimeter of irregular shapes.

To solve the problem, we need to calculate the area and perimeter for each of the given shapes. Let's go through each shape step by step.

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Shape 1:

#### Dimensions:
- Top side: 10 cm
- Left side: 3 cm
- Right side: 7 cm
- Bottom side: 5 cm
- Inner horizontal segment: 4 cm

#### Step 1: Calculate the missing side
The total length of the bottom side is 5 cm. The inner horizontal segment is 4 cm, so the remaining part of the bottom side is:
\[ 5 \text{ cm} - 4 \text{ cm} = 1 \text{ cm} \]

#### Step 2: Calculate the area
The shape can be divided into two rectangles:
1. Top rectangle: \( 10 \text{ cm} \times 3 \text{ cm} \)
2. Bottom rectangle: \( 5 \text{ cm} \times 4 \text{ cm} \)

Area of the top rectangle:
\[ 10 \text{ cm} \times 3 \text{ cm} = 30 \text{ cm}^2 \]

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

Total area:
\[ 30 \text{ cm}^2 + 20 \text{ cm}^2 = 50 \text{ cm}^2 \]

#### Step 3: Calculate the perimeter
The perimeter is the sum of all the outer sides:
\[ 10 \text{ cm} + 3 \text{ cm} + 7 \text{ cm} + 5 \text{ cm} + 4 \text{ cm} + 1 \text{ cm} = 30 \text{ cm} \]

#### Final Answer for Shape 1:
\[ \text{Area} = 50 \text{ cm}^2, \quad \text{Perimeter} = 30 \text{ cm} \]

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Shape 2:

#### Dimensions:
- Top side: 6 mm
- Right side: 6 mm
- Bottom side: 10 mm
- Left side: 8 mm
- Inner vertical segment: 2 mm (since \( 8 \text{ mm} - 6 \text{ mm} = 2 \text{ mm} \))

#### Step 1: Calculate the missing side
The inner vertical segment is 2 mm, and the total height is 8 mm. The remaining part of the left side is:
\[ 8 \text{ mm} - 2 \text{ mm} = 6 \text{ mm} \]

#### Step 2: Calculate the area
The shape can be divided into three rectangles:
1. Top rectangle: \( 6 \text{ mm} \times 2 \text{ mm} \)
2. Middle rectangle: \( 4 \text{ mm} \times 2 \text{ mm} \)
3. Bottom rectangle: \( 10 \text{ mm} \times 6 \text{ mm} \)

Area of the top rectangle:
\[ 6 \text{ mm} \times 2 \text{ mm} = 12 \text{ mm}^2 \]

Area of the middle rectangle:
\[ 4 \text{ mm} \times 2 \text{ mm} = 8 \text{ mm}^2 \]

Area of the bottom rectangle:
\[ 10 \text{ mm} \times 6 \text{ mm} = 60 \text{ mm}^2 \]

Total area:
\[ 12 \text{ mm}^2 + 8 \text{ mm}^2 + 60 \text{ mm}^2 = 80 \text{ mm}^2 \]

#### Step 3: Calculate the perimeter
The perimeter is the sum of all the outer sides:
\[ 6 \text{ mm} + 2 \text{ mm} + 4 \text{ mm} + 2 \text{ mm} + 6 \text{ mm} + 10 \text{ mm} + 6 \text{ mm} + 8 \text{ mm} = 44 \text{ mm} \]

#### Final Answer for Shape 2:
\[ \text{Area} = 80 \text{ mm}^2, \quad \text{Perimeter} = 44 \text{ mm} \]

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Shape 3:

#### Dimensions:
- Top side: 5 m
- Left side: 6 m
- Bottom side: 8 m
- Right side: 3 m
- Inner vertical segment: 3 m (since \( 6 \text{ m} - 3 \text{ m} = 3 \text{ m} \))

#### Step 1: Calculate the missing side
The inner vertical segment is 3 m, and the total height is 6 m. The remaining part of the left side is:
\[ 6 \text{ m} - 3 \text{ m} = 3 \text{ m} \]

#### Step 2: Calculate the area
The shape can be divided into two rectangles:
1. Top rectangle: \( 5 \text{ m} \times 3 \text{ m} \)
2. Bottom rectangle: \( 8 \text{ m} \times 3 \text{ m} \)

Area of the top rectangle:
\[ 5 \text{ m} \times 3 \text{ m} = 15 \text{ m}^2 \]

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

Total area:
\[ 15 \text{ m}^2 + 24 \text{ m}^2 = 39 \text{ m}^2 \]

#### Step 3: Calculate the perimeter
The perimeter is the sum of all the outer sides:
\[ 5 \text{ m} + 3 \text{ m} + 3 \text{ m} + 8 \text{ m} + 3 \text{ m} + 6 \text{ m} = 28 \text{ m} \]

#### Final Answer for Shape 3:
\[ \text{Area} = 39 \text{ m}^2, \quad \text{Perimeter} = 28 \text{ m} \]

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Shape 4:

#### Dimensions:
- Top side: 6 cm
- Right side: 4 cm
- Bottom side: 5 cm
- Left side: 8 cm
- Inner horizontal segment: 3 cm (since \( 8 \text{ cm} - 5 \text{ cm} = 3 \text{ cm} \))

#### Step 1: Calculate the missing side
The inner horizontal segment is 3 cm, and the total width is 8 cm. The remaining part of the left side is:
\[ 8 \text{ cm} - 3 \text{ cm} = 5 \text{ cm} \]

#### Step 2: Calculate the area
The shape can be divided into two rectangles:
1. Top rectangle: \( 6 \text{ cm} \times 5 \text{ cm} \)
2. Bottom rectangle: \( 5 \text{ cm} \times 3 \text{ cm} \)

Area of the top rectangle:
\[ 6 \text{ cm} \times 5 \text{ cm} = 30 \text{ cm}^2 \]

Area of the bottom rectangle:
\[ 5 \text{ cm} \times 3 \text{ cm} = 15 \text{ cm}^2 \]

Total area:
\[ 30 \text{ cm}^2 + 15 \text{ cm}^2 = 45 \text{ cm}^2 \]

#### Step 3: Calculate the perimeter
The perimeter is the sum of all the outer sides:
\[ 6 \text{ cm} + 5 \text{ cm} + 3 \text{ cm} + 5 \text{ cm} + 4 \text{ cm} + 8 \text{ cm} = 31 \text{ cm} \]

#### Final Answer for Shape 4:
\[ \text{Area} = 45 \text{ cm}^2, \quad \text{Perimeter} = 31 \text{ cm} \]

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Final Answers:

1. \( \text{Area} = 50 \text{ cm}^2, \quad \text{Perimeter} = 30 \text{ cm} \)
2. \( \text{Area} = 80 \text{ mm}^2, \quad \text{Perimeter} = 44 \text{ mm} \)
3. \( \text{Area} = 39 \text{ m}^2, \quad \text{Perimeter} = 28 \text{ m} \)
4. \( \text{Area} = 45 \text{ cm}^2, \quad \text{Perimeter} = 31 \text{ cm} \)

\[
\boxed{
\begin{array}{ll}
1) & \text{Area} = 50 \text{ cm}^2, \quad \text{Perimeter} = 30 \text{ cm} \\
2) & \text{Area} = 80 \text{ mm}^2, \quad \text{Perimeter} = 44 \text{ mm} \\
3) & \text{Area} = 39 \text{ m}^2, \quad \text{Perimeter} = 28 \text{ m} \\
4) & \text{Area} = 45 \text{ cm}^2, \quad \text{Perimeter} = 31 \text{ cm} \\
\end{array}
}
\]