Areas of Irregular Shapes (Rectilinear Figures): Worksheets - Free Printable

Problem Overview:

The task involves finding the area of irregular shapes by dividing them into simpler rectangular parts and calculating the area of each part. The formula for the area of a rectangle is:

\[
\text{Area} = \text{Length} \times \text{Width}
\]

We will solve each shape step by step.

---

Shape 1:

#### Description:
- The shape is divided into two rectangles.
- Rectangle 1: Top-left section
- Length = 6 cm
- Width = 5 cm
- Rectangle 2: Bottom-right section
- Length = 3 cm
- Width = 4 cm

#### Calculation:
1. Rectangle 1:
\[
\text{Area}_1 = 6 \, \text{cm} \times 5 \, \text{cm} = 30 \, \text{cm}^2
\]

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

3. Total Area:
\[
\text{Total Area} = \text{Area}_1 + \text{Area}_2 = 30 \, \text{cm}^2 + 12 \, \text{cm}^2 = 42 \, \text{cm}^2
\]

#### Final Answer for Shape 1:
\[
\boxed{42 \, \text{cm}^2}
\]

---

Shape 2:

#### Description:
- The shape is divided into three rectangles.
- Rectangle 1: Top-left section
- Length = 4 mm
- Width = 3 mm
- Rectangle 2: Top-right section
- Length = 4 mm
- Width = 3 mm
- Rectangle 3: Bottom section
- Length = 12 mm
- Width = 6 mm

#### Calculation:
1. Rectangle 1:
\[
\text{Area}_1 = 4 \, \text{mm} \times 3 \, \text{mm} = 12 \, \text{mm}^2
\]

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

3. Rectangle 3:
\[
\text{Area}_3 = 12 \, \text{mm} \times 6 \, \text{mm} = 72 \, \text{mm}^2
\]

4. Total Area:
\[
\text{Total Area} = \text{Area}_1 + \text{Area}_2 + \text{Area}_3 = 12 \, \text{mm}^2 + 12 \, \text{mm}^2 + 72 \, \text{mm}^2 = 96 \, \text{mm}^2
\]

#### Final Answer for Shape 2:
\[
\boxed{96 \, \text{mm}^2}
\]

---

Shape 3:

#### Description:
- The shape is divided into three rectangles.
- Rectangle 1: Top-left section
- Length = 4 m
- Width = 1 m
- Rectangle 2: Middle section
- Length = 4 m
- Width = 4 m
- Rectangle 3: Bottom-right section
- Length = 5 m
- Width = 4 m

#### Calculation:
1. Rectangle 1:
\[
\text{Area}_1 = 4 \, \text{m} \times 1 \, \text{m} = 4 \, \text{m}^2
\]

2. Rectangle 2:
\[
\text{Area}_2 = 4 \, \text{m} \times 4 \, \text{m} = 16 \, \text{m}^2
\]

3. Rectangle 3:
\[
\text{Area}_3 = 5 \, \text{m} \times 4 \, \text{m} = 20 \, \text{m}^2
\]

4. Total Area:
\[
\text{Total Area} = \text{Area}_1 + \text{Area}_2 + \text{Area}_3 = 4 \, \text{m}^2 + 16 \, \text{m}^2 + 20 \, \text{m}^2 = 40 \, \text{m}^2
\]

#### Final Answer for Shape 3:
\[
\boxed{40 \, \text{m}^2}
\]

---

Shape 4:

#### Description:
- The shape is divided into four rectangles.
- Rectangle 1: Top-left section
- Length = 2 cm
- Width = 3 cm
- Rectangle 2: Top-right section
- Length = 2 cm
- Width = 3 cm
- Rectangle 3: Bottom-left section
- Length = 5 cm
- Width = 2 cm
- Rectangle 4: Bottom-right section
- Length = 9 cm
- Width = 3 cm

#### Calculation:
1. Rectangle 1:
\[
\text{Area}_1 = 2 \, \text{cm} \times 3 \, \text{cm} = 6 \, \text{cm}^2
\]

2. Rectangle 2:
\[
\text{Area}_2 = 2 \, \text{cm} \times 3 \, \text{cm} = 6 \, \text{cm}^2
\]

3. Rectangle 3:
\[
\text{Area}_3 = 5 \, \text{cm} \times 2 \, \text{cm} = 10 \, \text{cm}^2
\]

4. Rectangle 4:
\[
\text{Area}_4 = 9 \, \text{cm} \times 3 \, \text{cm} = 27 \, \text{cm}^2
\]

5. Total Area:
\[
\text{Total Area} = \text{Area}_1 + \text{Area}_2 + \text{Area}_3 + \text{Area}_4 = 6 \, \text{cm}^2 + 6 \, \text{cm}^2 + 10 \, \text{cm}^2 + 27 \, \text{cm}^2 = 49 \, \text{cm}^2
\]

#### Final Answer for Shape 4:
\[
\boxed{49 \, \text{cm}^2}
\]

---

Final Answers:

1. \(\boxed{42 \, \text{cm}^2}\)
2. \(\boxed{96 \, \text{mm}^2}\)
3. \(\boxed{40 \, \text{m}^2}\)
4. \(\boxed{49 \, \text{cm}^2}\)