Practice worksheet for calculating the area of irregular shapes using given dimensions.

The task in the image involves calculating the area of various irregular shapes. Each shape is labeled with dimensions, and you need to use these dimensions to compute the area for each shape. Below, I will solve the problem step by step for each shape.

---

Shape 1: Trapezoid

#### Dimensions:
- Top base (\( b_1 \)): \( 120 \, \text{mm} \)
- Bottom base (\( b_2 \)): \( 250 \, \text{mm} \)
- Height (\( h \)): \( 180 \, \text{mm} \)

#### Formula for the area of a trapezoid:
\[
\text{Area} = \frac{1}{2} \times (b_1 + b_2) \times h
\]

#### Substituting the values:
\[
\text{Area} = \frac{1}{2} \times (120 + 250) \times 180
\]
\[
\text{Area} = \frac{1}{2} \times 370 \times 180
\]
\[
\text{Area} = 185 \times 180
\]
\[
\text{Area} = 33,300 \, \text{mm}^2
\]

---

Shape 2: Rectangle with a semicircle on top

#### Dimensions:
- Rectangle:
- Length (\( l \)): \( 160 \, \text{mm} \)
- Width (\( w \)): \( 40 \, \text{mm} \)
- Semicircle:
- Diameter (\( d \)): \( 40 \, \text{mm} \)
- Radius (\( r \)): \( \frac{d}{2} = 20 \, \text{mm} \)

#### Area of the rectangle:
\[
\text{Area}_{\text{rectangle}} = l \times w = 160 \times 40 = 6,400 \, \text{mm}^2
\]

#### Area of the semicircle:
\[
\text{Area}_{\text{semicircle}} = \frac{1}{2} \pi r^2 = \frac{1}{2} \pi (20)^2 = \frac{1}{2} \pi \times 400 = 200\pi \, \text{mm}^2
\]

Using \( \pi \approx 3.14 \):
\[
\text{Area}_{\text{semicircle}} \approx 200 \times 3.14 = 628 \, \text{mm}^2
\]

#### Total area:
\[
\text{Total Area} = \text{Area}_{\text{rectangle}} + \text{Area}_{\text{semicircle}}
\]
\[
\text{Total Area} = 6,400 + 628 = 7,028 \, \text{mm}^2
\]

---

Shape 3: Circle

#### Dimensions:
- Diameter (\( d \)): \( 120 \, \text{mm} \)
- Radius (\( r \)): \( \frac{d}{2} = 60 \, \text{mm} \)

#### Formula for the area of a circle:
\[
\text{Area} = \pi r^2
\]

#### Substituting the values:
\[
\text{Area} = \pi (60)^2 = 3,600\pi \, \text{mm}^2
\]

Using \( \pi \approx 3.14 \):
\[
\text{Area} \approx 3,600 \times 3.14 = 11,304 \, \text{mm}^2
\]

---

Shape 4: Triangle

#### Dimensions:
- Base (\( b \)): \( 150 \, \text{mm} \)
- Height (\( h \)): \( 90 \, \text{mm} \)

#### Formula for the area of a triangle:
\[
\text{Area} = \frac{1}{2} \times b \times h
\]

#### Substituting the values:
\[
\text{Area} = \frac{1}{2} \times 150 \times 90
\]
\[
\text{Area} = 75 \times 90
\]
\[
\text{Area} = 6,750 \, \text{mm}^2
\]

---

Shape 5: Parallelogram

#### Dimensions:
- Base (\( b \)): \( 180 \, \text{mm} \)
- Height (\( h \)): \( 120 \, \text{mm} \)

#### Formula for the area of a parallelogram:
\[
\text{Area} = b \times h
\]

#### Substituting the values:
\[
\text{Area} = 180 \times 120 = 21,600 \, \text{mm}^2
\]

---

Shape 6: Sector of a Circle

#### Dimensions:
- Radius (\( r \)): \( 80 \, \text{mm} \)
- Central angle (\( \theta \)): \( 120^\circ \)

#### Formula for the area of a sector:
\[
\text{Area} = \frac{\theta}{360^\circ} \times \pi r^2
\]

#### Substituting the values:
\[
\text{Area} = \frac{120^\circ}{360^\circ} \times \pi (80)^2
\]
\[
\text{Area} = \frac{1}{3} \times \pi \times 6,400
\]
\[
\text{Area} = \frac{6,400\pi}{3}
\]

Using \( \pi \approx 3.14 \):
\[
\text{Area} \approx \frac{6,400 \times 3.14}{3} = \frac{20,096}{3} \approx 6,698.67 \, \text{mm}^2
\]

---

Shape 7: Trapezoid

#### Dimensions:
- Top base (\( b_1 \)): \( 120 \, \text{mm} \)
- Bottom base (\( b_2 \)): \( 200 \, \text{mm} \)
- Height (\( h \)): \( 150 \, \text{mm} \)

#### Formula for the area of a trapezoid:
\[
\text{Area} = \frac{1}{2} \times (b_1 + b_2) \times h
\]

#### Substituting the values:
\[
\text{Area} = \frac{1}{2} \times (120 + 200) \times 150
\]
\[
\text{Area} = \frac{1}{2} \times 320 \times 150
\]
\[
\text{Area} = 160 \times 150
\]
\[
\text{Area} = 24,000 \, \text{mm}^2
\]

---

Shape 8: Rectangle

#### Dimensions:
- Length (\( l \)): \( 200 \, \text{mm} \)
- Width (\( w \)): \( 80 \, \text{mm} \)

#### Formula for the area of a rectangle:
\[
\text{Area} = l \times w
\]

#### Substituting the values:
\[
\text{Area} = 200 \times 80 = 16,000 \, \text{mm}^2
\]

---

Final Answers:

1. \( 33,300 \, \text{mm}^2 \)
2. \( 7,028 \, \text{mm}^2 \)
3. \( 11,304 \, \text{mm}^2 \)
4. \( 6,750 \, \text{mm}^2 \)
5. \( 21,600 \, \text{mm}^2 \)
6. \( 6,698.67 \, \text{mm}^2 \)
7. \( 24,000 \, \text{mm}^2 \)
8. \( 16,000 \, \text{mm}^2 \)

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Boxed Final Answer:

\[
\boxed{33,300, 7,028, 11,304, 6,750, 21,600, 6,698.67, 24,000, 16,000}
\]