Area Worksheets - Free Printable

To solve the problem of finding the area of each shape by dividing them into rectangles, we will break down each shape into simpler rectangular components and calculate their areas individually. Then, we will sum up the areas of these rectangles to get the total area of the shape.

Problem 1:

The shape is divided into two rectangles:
- Rectangle 1: Top rectangle with dimensions \(9 \, \text{cm} \times 3 \, \text{cm}\)
- Rectangle 2: Bottom rectangle with dimensions \(4 \, \text{cm} \times 8 \, \text{cm}\)

#### Step-by-Step Calculation:
1. Area of Rectangle 1:
\[
\text{Area}_1 = 9 \, \text{cm} \times 3 \, \text{cm} = 27 \, \text{cm}^2
\]

2. Area of Rectangle 2:
\[
\text{Area}_2 = 4 \, \text{cm} \times 8 \, \text{cm} = 32 \, \text{cm}^2
\]

3. Total Area:
\[
\text{Total Area} = \text{Area}_1 + \text{Area}_2 = 27 \, \text{cm}^2 + 32 \, \text{cm}^2 = 59 \, \text{cm}^2
\]

Answer for Problem 1:
\[
\boxed{59 \, \text{cm}^2}
\]

---

Problem 2:

The shape is divided into two rectangles:
- Rectangle 1: Left rectangle with dimensions \(6 \, \text{mm} \times 20 \, \text{mm}\)
- Rectangle 2: Right rectangle with dimensions \(10 \, \text{mm} \times 15 \, \text{mm}\)

#### Step-by-Step Calculation:
1. Area of Rectangle 1:
\[
\text{Area}_1 = 6 \, \text{mm} \times 20 \, \text{mm} = 120 \, \text{mm}^2
\]

2. Area of Rectangle 2:
\[
\text{Area}_2 = 10 \, \text{mm} \times 15 \, \text{mm} = 150 \, \text{mm}^2
\]

3. Total Area:
\[
\text{Total Area} = \text{Area}_1 + \text{Area}_2 = 120 \, \text{mm}^2 + 150 \, \text{mm}^2 = 270 \, \text{mm}^2
\]

Answer for Problem 2:
\[
\boxed{270 \, \text{mm}^2}
\]

---

Problem 3:

The shape is divided into three rectangles:
- Rectangle 1: Top-left rectangle with dimensions \(8 \, \text{cm} \times 3 \, \text{cm}\)
- Rectangle 2: Middle rectangle with dimensions \(4 \, \text{cm} \times 3 \, \text{cm}\)
- Rectangle 3: Bottom rectangle with dimensions \(12 \, \text{cm} \times 5 \, \text{cm}\)

#### Step-by-Step Calculation:
1. Area of Rectangle 1:
\[
\text{Area}_1 = 8 \, \text{cm} \times 3 \, \text{cm} = 24 \, \text{cm}^2
\]

2. Area of Rectangle 2:
\[
\text{Area}_2 = 4 \, \text{cm} \times 3 \, \text{cm} = 12 \, \text{cm}^2
\]

3. Area of Rectangle 3:
\[
\text{Area}_3 = 12 \, \text{cm} \times 5 \, \text{cm} = 60 \, \text{cm}^2
\]

4. Total Area:
\[
\text{Total Area} = \text{Area}_1 + \text{Area}_2 + \text{Area}_3 = 24 \, \text{cm}^2 + 12 \, \text{cm}^2 + 60 \, \text{cm}^2 = 96 \, \text{cm}^2
\]

Answer for Problem 3:
\[
\boxed{96 \, \text{cm}^2}
\]

---

Problem 4:

The shape is divided into three rectangles:
- Rectangle 1: Top rectangle with dimensions \(1.5 \, \text{m} \times 2 \, \text{m}\)
- Rectangle 2: Middle rectangle with dimensions \(3.5 \, \text{m} \times 2 \, \text{m}\)
- Rectangle 3: Bottom rectangle with dimensions \(5 \, \text{m} \times 1.5 \, \text{m}\)

#### Step-by-Step Calculation:
1. Area of Rectangle 1:
\[
\text{Area}_1 = 1.5 \, \text{m} \times 2 \, \text{m} = 3 \, \text{m}^2
\]

2. Area of Rectangle 2:
\[
\text{Area}_2 = 3.5 \, \text{m} \times 2 \, \text{m} = 7 \, \text{m}^2
\]

3. Area of Rectangle 3:
\[
\text{Area}_3 = 5 \, \text{m} \times 1.5 \, \text{m} = 7.5 \, \text{m}^2
\]

4. Total Area:
\[
\text{Total Area} = \text{Area}_1 + \text{Area}_2 + \text{Area}_3 = 3 \, \text{m}^2 + 7 \, \text{m}^2 + 7.5 \, \text{m}^2 = 17.5 \, \text{m}^2
\]

Answer for Problem 4:
\[
\boxed{17.5 \, \text{m}^2}
\]

---

Final Answers:

1. \(\boxed{59 \, \text{cm}^2}\)
2. \(\boxed{270 \, \text{mm}^2}\)
3. \(\boxed{96 \, \text{cm}^2}\)
4. \(\boxed{17.5 \, \text{m}^2}\)