This worksheet, titled 'Compound Shapes (A)', presents six problems where students must calculate the area and perimeter of various complex geometric figures.

To solve the problem of finding the area and perimeter of the given compound shapes, we will break each shape into simpler rectangles, calculate their areas and perimeters individually, and then combine them as necessary. Let's go through each shape step by step.

---

Shape 1:

#### Step 1: Identify the rectangles
- Rectangle (A): Dimensions are \(4 \, \text{cm} \times 3 \, \text{cm}\)
- Rectangle (B): Dimensions are \(8 \, \text{cm} \times 3 \, \text{cm}\)

#### Step 2: Calculate the area of each rectangle
- Area of Rectangle (A):
\[
\text{Area}_A = 4 \, \text{cm} \times 3 \, \text{cm} = 12 \, \text{cm}^2
\]
- Area of Rectangle (B):
\[
\text{Area}_B = 8 \, \text{cm} \times 3 \, \text{cm} = 24 \, \text{cm}^2
\]

#### Step 3: Calculate the total area
\[
\text{Total Area} = \text{Area}_A + \text{Area}_B = 12 \, \text{cm}^2 + 24 \, \text{cm}^2 = 36 \, \text{cm}^2
\]

#### Step 4: Calculate the perimeter
The perimeter is the sum of all outer sides:
\[
\text{Perimeter} = 6 \, \text{cm} + 8 \, \text{cm} + 3 \, \text{cm} + 3 \, \text{cm} + 4 \, \text{cm} + 4 \, \text{cm} = 28 \, \text{cm}
\]

#### Final Answers for Shape 1:
\[
\boxed{
\begin{aligned}
&\text{Area of rectangle (A)} = 12 \, \text{cm}^2 \\
&\text{Area of rectangle (B)} = 24 \, \text{cm}^2 \\
&\text{Total area} = 36 \, \text{cm}^2 \\
&\text{Perimeter} = 28 \, \text{cm}
\end{aligned}
}
\]

---

Shape 2:

#### Step 1: Identify the rectangles
- Rectangle (A): Dimensions are \(7 \, \text{cm} \times 3 \, \text{cm}\)
- Rectangle (B): Dimensions are \(6 \, \text{cm} \times 4 \, \text{cm}\)

#### Step 2: Calculate the area of each rectangle
- Area of Rectangle (A):
\[
\text{Area}_A = 7 \, \text{cm} \times 3 \, \text{cm} = 21 \, \text{cm}^2
\]
- Area of Rectangle (B):
\[
\text{Area}_B = 6 \, \text{cm} \times 4 \, \text{cm} = 24 \, \text{cm}^2
\]

#### Step 3: Calculate the total area
\[
\text{Total Area} = \text{Area}_A + \text{Area}_B = 21 \, \text{cm}^2 + 24 \, \text{cm}^2 = 45 \, \text{cm}^2
\]

#### Step 4: Calculate the perimeter
The perimeter is the sum of all outer sides:
\[
\text{Perimeter} = 7 \, \text{cm} + 7 \, \text{cm} + 6 \, \text{cm} + 6 \, \text{cm} + 4 \, \text{cm} + 4 \, \text{cm} + 1 \, \text{cm} + 3 \, \text{cm} = 40 \, \text{cm}
\]

#### Final Answers for Shape 2:
\[
\boxed{
\begin{aligned}
&\text{Area of rectangle (A)} = 21 \, \text{cm}^2 \\
&\text{Area of rectangle (B)} = 24 \, \text{cm}^2 \\
&\text{Total area} = 45 \, \text{cm}^2 \\
&\text{Perimeter} = 40 \, \text{cm}
\end{aligned}
}
\]

---

Shape 3:

#### Step 1: Identify the rectangles
- Rectangle (A): Dimensions are \(10 \, \text{cm} \times 2 \, \text{cm}\)
- Rectangle (B): Dimensions are \(7 \, \text{cm} \times 3 \, \text{cm}\)

#### Step 2: Calculate the area of each rectangle
- Area of Rectangle (A):
\[
\text{Area}_A = 10 \, \text{cm} \times 2 \, \text{cm} = 20 \, \text{cm}^2
\]
- Area of Rectangle (B):
\[
\text{Area}_B = 7 \, \text{cm} \times 3 \, \text{cm} = 21 \, \text{cm}^2
\]

#### Step 3: Calculate the total area
\[
\text{Total Area} = \text{Area}_A + \text{Area}_B = 20 \, \text{cm}^2 + 21 \, \text{cm}^2 = 41 \, \text{cm}^2
\]

#### Step 4: Calculate the perimeter
The perimeter is the sum of all outer sides:
\[
\text{Perimeter} = 10 \, \text{cm} + 2 \, \text{cm} + 7 \, \text{cm} + 3 \, \text{cm} + 9 \, \text{cm} + 7 \, \text{cm} = 38 \, \text{cm}
\]

#### Final Answers for Shape 3:
\[
\boxed{
\begin{aligned}
&\text{Area of rectangle (A)} = 20 \, \text{cm}^2 \\
&\text{Area of rectangle (B)} = 21 \, \text{cm}^2 \\
&\text{Total area} = 41 \, \text{cm}^2 \\
&\text{Perimeter} = 38 \, \text{cm}
\end{aligned}
}
\]

---

Shape 4:

#### Step 1: Identify the rectangles
- Rectangle (A): Dimensions are \(12 \, \text{cm} \times 4 \, \text{cm}\)
- Rectangle (B): Dimensions are \(5 \, \text{cm} \times 9 \, \text{cm}\)

#### Step 2: Calculate the area of each rectangle
- Area of Rectangle (A):
\[
\text{Area}_A = 12 \, \text{cm} \times 4 \, \text{cm} = 48 \, \text{cm}^2
\]
- Area of Rectangle (B):
\[
\text{Area}_B = 5 \, \text{cm} \times 9 \, \text{cm} = 45 \, \text{cm}^2
\]

#### Step 3: Calculate the total area
\[
\text{Total Area} = \text{Area}_A + \text{Area}_B = 48 \, \text{cm}^2 + 45 \, \text{cm}^2 = 93 \, \text{cm}^2
\]

#### Step 4: Calculate the perimeter
The perimeter is the sum of all outer sides:
\[
\text{Perimeter} = 12 \, \text{cm} + 4 \, \text{cm} + 4 \, \text{cm} + 5 \, \text{cm} + 5 \, \text{cm} + 9 \, \text{cm} + 9 \, \text{cm} + 2 \, \text{cm} = 50 \, \text{cm}
\]

#### Final Answers for Shape 4:
\[
\boxed{
\begin{aligned}
&\text{Total area} = 93 \, \text{cm}^2 \\
&\text{Perimeter} = 50 \, \text{cm}
\end{aligned}
}
\]

---

Shape 5:

#### Step 1: Identify the rectangles
- Rectangle (A): Dimensions are \(15 \, \text{cm} \times 11 \, \text{cm}\)
- Rectangle (B): Dimensions are \(7 \, \text{cm} \times 6 \, \text{cm}\)
- Rectangle (C): Dimensions are \(11 \, \text{cm} \times 4 \, \text{cm}\)

#### Step 2: Calculate the area of each rectangle
- Area of Rectangle (A):
\[
\text{Area}_A = 15 \, \text{cm} \times 11 \, \text{cm} = 165 \, \text{cm}^2
\]
- Area of Rectangle (B):
\[
\text{Area}_B = 7 \, \text{cm} \times 6 \, \text{cm} = 42 \, \text{cm}^2
\]
- Area of Rectangle (C):
\[
\text{Area}_C = 11 \, \text{cm} \times 4 \, \text{cm} = 44 \, \text{cm}^2
\]

#### Step 3: Calculate the total area
\[
\text{Total Area} = \text{Area}_A + \text{Area}_B + \text{Area}_C = 165 \, \text{cm}^2 + 42 \, \text{cm}^2 + 44 \, \text{cm}^2 = 251 \, \text{cm}^2
\]

#### Step 4: Calculate the perimeter
The perimeter is the sum of all outer sides:
\[
\text{Perimeter} = 15 \, \text{cm} + 11 \, \text{cm} + 11 \, \text{cm} + 4 \, \text{cm} + 4 \, \text{cm} + 7 \, \text{cm} + 6 \, \text{cm} + 6 \, \text{cm} + 7 \, \text{cm} + 4 \, \text{cm} = 75 \, \text{cm}
\]

#### Final Answers for Shape 5:
\[
\boxed{
\begin{aligned}
&\text{Total area} = 251 \, \text{cm}^2 \\
&\text{Perimeter} = 75 \, \text{cm}
\end{aligned}
}
\]

---

Shape 6:

#### Step 1: Identify the rectangles
- Rectangle (A): Dimensions are \(13 \, \text{cm} \times 2 \, \text{cm}\)
- Rectangle (B): Dimensions are \(10 \, \text{cm} \times 7 \, \text{cm}\)
- Rectangle (C): Dimensions are \(5 \, \text{cm} \times 3 \, \text{cm}\)

#### Step 2: Calculate the area of each rectangle
- Area of Rectangle (A):
\[
\text{Area}_A = 13 \, \text{cm} \times 2 \, \text{cm} = 26 \, \text{cm}^2
\]
- Area of Rectangle (B):
\[
\text{Area}_B = 10 \, \text{cm} \times 7 \, \text{cm} = 70 \, \text{cm}^2
\]
- Area of Rectangle (C):
\[
\text{Area}_C = 5 \, \text{cm} \times 3 \, \text{cm} = 15 \, \text{cm}^2
\]

#### Step 3: Calculate the total area
\[
\text{Total Area} = \text{Area}_A + \text{Area}_B + \text{Area}_C = 26 \, \text{cm}^2 + 70 \, \text{cm}^2 + 15 \, \text{cm}^2 = 111 \, \text{cm}^2
\]

#### Step 4: Calculate the perimeter
The perimeter is the sum of all outer sides:
\[
\text{Perimeter} = 13 \, \text{cm} + 2 \, \text{cm} + 2 \, \text{cm} + 6 \, \text{cm} + 6 \, \text{cm} + 10 \, \text{cm} + 7 \, \text{cm} + 7 \, \text{cm} + 5 \, \text{cm} + 3 \, \text{cm} + 3 \, \text{cm} + 2 \, \text{cm} = 68 \, \text{cm}
\]

#### Final Answers for Shape 6:
\[
\boxed{
\begin{aligned}
&\text{Total area} = 111 \, \text{cm}^2 \\
&\text{Perimeter} = 68 \, \text{cm}
\end{aligned}
}
\]

---

Final Summary of All Shapes:

\[
\boxed{
\begin{aligned}
&\text{Shape 1:} \quad \text{Total area} = 36 \, \text{cm}^2, \, \text{Perimeter} = 28 \, \text{cm} \\
&\text{Shape 2:} \quad \text{Total area} = 45 \, \text{cm}^2, \, \text{Perimeter} = 40 \, \text{cm} \\
&\text{Shape 3:} \quad \text{Total area} = 41 \, \text{cm}^2, \, \text{Perimeter} = 38 \, \text{cm} \\
&\text{Shape 4:} \quad \text{Total area} = 93 \, \text{cm}^2, \, \text{Perimeter} = 50 \, \text{cm} \\
&\text{Shape 5:} \quad \text{Total area} = 251 \, \text{cm}^2, \, \text{Perimeter} = 75 \, \text{cm} \\
&\text{Shape 6:} \quad \text{Total area} = 111 \, \text{cm}^2, \, \text{Perimeter} = 68 \, \text{cm}
\end{aligned}
}
\]