Area of Compound Shapes with Rectangles - Maths with Mum - Free Printable

To solve the problem of calculating the areas of the compound shapes, we need to break each shape into simpler geometric figures (like rectangles) and then sum their areas. Let's go through each part step by step.

---

Part (a)

The shape is composed of two rectangles:
1. A larger rectangle with dimensions \(8 \, \text{cm} \times 6 \, \text{cm}\).
2. A smaller rectangle with dimensions \(4 \, \text{cm} \times 2 \, \text{cm}\).

#### Step 1: Calculate the area of the larger rectangle
\[
\text{Area of larger rectangle} = 8 \, \text{cm} \times 6 \, \text{cm} = 48 \, \text{cm}^2
\]

#### Step 2: Calculate the area of the smaller rectangle
\[
\text{Area of smaller rectangle} = 4 \, \text{cm} \times 2 \, \text{cm} = 8 \, \text{cm}^2
\]

#### Step 3: Sum the areas
\[
\text{Total area} = 48 \, \text{cm}^2 + 8 \, \text{cm}^2 = 56 \, \text{cm}^2
\]

Answer for (a):
\[
\boxed{56}
\]

---

Part (b)

The shape is composed of two rectangles:
1. A larger rectangle with dimensions \(12 \, \text{cm} \times 7 \, \text{cm}\).
2. A smaller rectangle with dimensions \(3 \, \text{cm} \times 4 \, \text{cm}\).

#### Step 1: Calculate the area of the larger rectangle
\[
\text{Area of larger rectangle} = 12 \, \text{cm} \times 7 \, \text{cm} = 84 \, \text{cm}^2
\]

#### Step 2: Calculate the area of the smaller rectangle
\[
\text{Area of smaller rectangle} = 3 \, \text{cm} \times 4 \, \text{cm} = 12 \, \text{cm}^2
\]

#### Step 3: Sum the areas
\[
\text{Total area} = 84 \, \text{cm}^2 + 12 \, \text{cm}^2 = 96 \, \text{cm}^2
\]

Answer for (b):
\[
\boxed{96}
\]

---

Part (c)

The shape is composed of two rectangles:
1. A larger rectangle with dimensions \(11 \, \text{cm} \times 6 \, \text{cm}\).
2. A smaller rectangle with dimensions \(7 \, \text{cm} \times 4 \, \text{cm}\).

#### Step 1: Calculate the area of the larger rectangle
\[
\text{Area of larger rectangle} = 11 \, \text{cm} \times 6 \, \text{cm} = 66 \, \text{cm}^2
\]

#### Step 2: Calculate the area of the smaller rectangle
\[
\text{Area of smaller rectangle} = 7 \, \text{cm} \times 4 \, \text{cm} = 28 \, \text{cm}^2
\]

#### Step 3: Sum the areas
\[
\text{Total area} = 66 \, \text{cm}^2 + 28 \, \text{cm}^2 = 94 \, \text{cm}^2
\]

Answer for (c):
\[
\boxed{94}
\]

---

Part (d)

The shape is composed of three rectangles:
1. A top rectangle with dimensions \(18 \, \text{cm} \times 8 \, \text{cm}\).
2. A middle rectangle with dimensions \(12 \, \text{cm} \times 6 \, \text{cm}\).
3. A bottom rectangle with dimensions \(6 \, \text{cm} \times 8 \, \text{cm}\).

#### Step 1: Calculate the area of the top rectangle
\[
\text{Area of top rectangle} = 18 \, \text{cm} \times 8 \, \text{cm} = 144 \, \text{cm}^2
\]

#### Step 2: Calculate the area of the middle rectangle
\[
\text{Area of middle rectangle} = 12 \, \text{cm} \times 6 \, \text{cm} = 72 \, \text{cm}^2
\]

#### Step 3: Calculate the area of the bottom rectangle
\[
\text{Area of bottom rectangle} = 6 \, \text{cm} \times 8 \, \text{cm} = 48 \, \text{cm}^2
\]

#### Step 4: Sum the areas
\[
\text{Total area} = 144 \, \text{cm}^2 + 72 \, \text{cm}^2 + 48 \, \text{cm}^2 = 264 \, \text{cm}^2
\]

Answer for (d):
\[
\boxed{264}
\]

---

Final Answers:

\[
\boxed{56, 96, 94, 264}
\]