Math worksheet for calculating the area and perimeter of irregular polygons, featuring eight different shapes with given dimensions.

To solve the problems of finding the area and perimeter of irregular polygons, we need to break each shape into simpler geometric shapes (like rectangles) and then calculate the area and perimeter step by step. Let's go through each problem:

---

Problem 1

Shape:
- A rectangle with a smaller rectangle cut out from one corner.
- Dimensions: Outer rectangle is \(18 \, \text{cm} \times 10 \, \text{cm}\).
- Inner rectangle dimensions: \(4 \, \text{cm} \times 8 \, \text{cm}\).

#### Area:
1. Area of the outer rectangle:
\[
\text{Area}_{\text{outer}} = 18 \times 10 = 180 \, \text{cm}^2
\]
2. Area of the inner rectangle:
\[
\text{Area}_{\text{inner}} = 4 \times 8 = 32 \, \text{cm}^2
\]
3. Total area:
\[
\text{Area} = \text{Area}_{\text{outer}} - \text{Area}_{\text{inner}} = 180 - 32 = 148 \, \text{cm}^2
\]

#### Perimeter:
1. The perimeter of the irregular shape is the sum of all its outer edges.
2. The shape has the following sides:
- Top: \(18 \, \text{cm}\)
- Bottom: \(18 \, \text{cm}\)
- Left side: \(10 \, \text{cm}\)
- Right side: \(10 \, \text{cm}\)
- Inner vertical cut: \(4 \, \text{cm}\)
- Inner horizontal cut: \(8 \, \text{cm}\)
3. Total perimeter:
\[
\text{Perimeter} = 18 + 18 + 10 + 10 + 4 + 8 = 68 \, \text{cm}
\]

Answer for Problem 1:
\[
\boxed{148 \, \text{cm}^2, 68 \, \text{cm}}
\]

---

Problem 2

Shape:
- A large rectangle with a smaller rectangle cut out from the middle.
- Dimensions: Outer rectangle is \(8.5 \, \text{in} \times 4 \, \text{in}\).
- Inner rectangle dimensions: \(6 \, \text{in} \times 2.5 \, \text{in}\).

#### Area:
1. Area of the outer rectangle:
\[
\text{Area}_{\text{outer}} = 8.5 \times 4 = 34 \, \text{in}^2
\]
2. Area of the inner rectangle:
\[
\text{Area}_{\text{inner}} = 6 \times 2.5 = 15 \, \text{in}^2
\]
3. Total area:
\[
\text{Area} = \text{Area}_{\text{outer}} - \text{Area}_{\text{inner}} = 34 - 15 = 19 \, \text{in}^2
\]

#### Perimeter:
1. The perimeter of the irregular shape is the sum of all its outer edges.
2. The shape has the following sides:
- Top: \(8.5 \, \text{in}\)
- Bottom: \(8.5 \, \text{in}\)
- Left side: \(4 \, \text{in}\)
- Right side: \(4 \, \text{in}\)
- Inner vertical cuts: \(2 \times 2.5 \, \text{in} = 5 \, \text{in}\)
- Inner horizontal cuts: \(2 \times 6 \, \text{in} = 12 \, \text{in}\)
3. Total perimeter:
\[
\text{Perimeter} = 8.5 + 8.5 + 4 + 4 + 5 + 12 = 32 \, \text{in}
\]

Answer for Problem 2:
\[
\boxed{19 \, \text{in}^2, 32 \, \text{in}}
\]

---

Problem 3

Shape:
- An L-shaped polygon.
- Dimensions:
- Top part: \(12 \, \text{in} \times 7 \, \text{in}\)
- Bottom part: \(19 \, \text{in} \times 6 \, \text{in}\)

#### Area:
1. Area of the top rectangle:
\[
\text{Area}_{\text{top}} = 12 \times 7 = 84 \, \text{in}^2
\]
2. Area of the bottom rectangle:
\[
\text{Area}_{\text{bottom}} = 19 \times 6 = 114 \, \text{in}^2
\]
3. Total area:
\[
\text{Area} = \text{Area}_{\text{top}} + \text{Area}_{\text{bottom}} = 84 + 114 = 198 \, \text{in}^2
\]

#### Perimeter:
1. The perimeter of the irregular shape is the sum of all its outer edges.
2. The shape has the following sides:
- Top: \(12 \, \text{in}\)
- Right side: \(7 \, \text{in}\)
- Bottom: \(19 \, \text{in}\)
- Left side: \(6 \, \text{in}\)
- Inner vertical cut: \(12 - 6 = 6 \, \text{in}\)
- Inner horizontal cut: \(19 - 7 = 12 \, \text{in}\)
3. Total perimeter:
\[
\text{Perimeter} = 12 + 7 + 19 + 6 + 6 + 12 = 62 \, \text{in}
\]

Answer for Problem 3:
\[
\boxed{198 \, \text{in}^2, 62 \, \text{in}}
\]

---

Problem 4

Shape:
- An irregular polygon with given side lengths.

#### Area:
1. Break the shape into two rectangles:
- Top rectangle: \(16.8 \, \text{ft} \times 8.1 \, \text{ft}\)
- Bottom rectangle: \(13.2 \, \text{ft} \times 5.1 \, \text{ft}\)
2. Area of the top rectangle:
\[
\text{Area}_{\text{top}} = 16.8 \times 8.1 = 136.08 \, \text{ft}^2
\]
3. Area of the bottom rectangle:
\[
\text{Area}_{\text{bottom}} = 13.2 \times 5.1 = 67.32 \, \text{ft}^2
\]
4. Total area:
\[
\text{Area} = \text{Area}_{\text{top}} + \text{Area}_{\text{bottom}} = 136.08 + 67.32 = 203.4 \, \text{ft}^2
\]

#### Perimeter:
1. Sum all the outer edges:
\[
\text{Perimeter} = 16.8 + 8.1 + 4.4 + 5.1 + 13.2 + 12.4 = 59.0 \, \text{ft}
\]

Answer for Problem 4:
\[
\boxed{203.4 \, \text{ft}^2, 59.0 \, \text{ft}}
\]

---

Problem 5

Shape:
- An irregular polygon with given side lengths.

#### Area:
1. Break the shape into two rectangles:
- Top rectangle: \(17.8 \, \text{in} \times 5.7 \, \text{in}\)
- Bottom rectangle: \(15.2 \, \text{in} \times 4.8 \, \text{in}\)
2. Area of the top rectangle:
\[
\text{Area}_{\text{top}} = 17.8 \times 5.7 = 101.46 \, \text{in}^2
\]
3. Area of the bottom rectangle:
\[
\text{Area}_{\text{bottom}} = 15.2 \times 4.8 = 72.96 \, \text{in}^2
\]
4. Total area:
\[
\text{Area} = \text{Area}_{\text{top}} + \text{Area}_{\text{bottom}} = 101.46 + 72.96 = 174.42 \, \text{in}^2
\]

#### Perimeter:
1. Sum all the outer edges:
\[
\text{Perimeter} = 17.8 + 5.7 + 6.5 + 4.8 + 15.2 + 6.5 = 56.5 \, \text{in}
\]

Answer for Problem 5:
\[
\boxed{174.42 \, \text{in}^2, 56.5 \, \text{in}}
\]

---

Problem 6

Shape:
- An irregular polygon with given side lengths.

#### Area:
1. Break the shape into two rectangles:
- Top rectangle: \(18.8 \, \text{ft} \times 5.5 \, \text{ft}\)
- Bottom rectangle: \(25.5 \, \text{ft} \times 4.2 \, \text{ft}\)
2. Area of the top rectangle:
\[
\text{Area}_{\text{top}} = 18.8 \times 5.5 = 103.4 \, \text{ft}^2
\]
3. Area of the bottom rectangle:
\[
\text{Area}_{\text{bottom}} = 25.5 \times 4.2 = 107.1 \, \text{ft}^2
\]
4. Total area:
\[
\text{Area} = \text{Area}_{\text{top}} + \text{Area}_{\text{bottom}} = 103.4 + 107.1 = 210.5 \, \text{ft}^2
\]

#### Perimeter:
1. Sum all the outer edges:
\[
\text{Perimeter} = 18.8 + 5.5 + 4.2 + 25.5 + 18.8 + 5.5 = 78.3 \, \text{ft}
\]

Answer for Problem 6:
\[
\boxed{210.5 \, \text{ft}^2, 78.3 \, \text{ft}}
\]

---

Problem 7

Shape:
- An irregular polygon with given side lengths.

#### Area:
1. Break the shape into three rectangles:
- Top rectangle: \(9 \, \text{cm} \times 6.8 \, \text{cm}\)
- Middle rectangle: \(5.5 \, \text{cm} \times 6.8 \, \text{cm}\)
- Bottom rectangle: \(16 \, \text{cm} \times 6.8 \, \text{cm}\)
2. Area of the top rectangle:
\[
\text{Area}_{\text{top}} = 9 \times 6.8 = 61.2 \, \text{cm}^2
\]
3. Area of the middle rectangle:
\[
\text{Area}_{\text{middle}} = 5.5 \times 6.8 = 37.4 \, \text{cm}^2
\]
4. Area of the bottom rectangle:
\[
\text{Area}_{\text{bottom}} = 16 \times 6.8 = 108.8 \, \text{cm}^2
\]
5. Total area:
\[
\text{Area} = \text{Area}_{\text{top}} + \text{Area}_{\text{middle}} + \text{Area}_{\text{bottom}} = 61.2 + 37.4 + 108.8 = 207.4 \, \text{cm}^2
\]

#### Perimeter:
1. Sum all the outer edges:
\[
\text{Perimeter} = 9 + 6.8 + 5.5 + 6.8 + 16 + 6.8 + 6.8 + 9 = 66.7 \, \text{cm}
\]

Answer for Problem 7:
\[
\boxed{207.4 \, \text{cm}^2, 66.7 \, \text{cm}}
\]

---

Problem 8

Shape:
- An irregular polygon with given side lengths.

#### Area:
1. Break the shape into three rectangles:
- Top rectangle: \(3.8 \, \text{m} \times 16.8 \, \text{m}\)
- Middle rectangle: \(4.4 \, \text{m} \times 8.8 \, \text{m}\)
- Bottom rectangle: \(4.4 \, \text{m} \times 3.8 \, \text{m}\)
2. Area of the top rectangle:
\[
\text{Area}_{\text{top}} = 3.8 \times 16.8 = 63.84 \, \text{m}^2
\]
3. Area of the middle rectangle:
\[
\text{Area}_{\text{middle}} = 4.4 \times 8.8 = 38.72 \, \text{m}^2
\]
4. Area of the bottom rectangle:
\[
\text{Area}_{\text{bottom}} = 4.4 \times 3.8 = 16.72 \, \text{m}^2
\]
5. Total area:
\[
\text{Area} = \text{Area}_{\text{top}} + \text{Area}_{\text{middle}} + \text{Area}_{\text{bottom}} = 63.84 + 38.72 + 16.72 = 119.28 \, \text{m}^2
\]

#### Perimeter:
1. Sum all the outer edges:
\[
\text{Perimeter} = 3.8 + 16.8 + 4.4 + 8.8 + 4.4 + 3.8 + 4.4 + 4.4 = 46.8 \, \text{m}
\]

Answer for Problem 8:
\[
\boxed{119.28 \, \text{m}^2, 46.8 \, \text{m}}
\]

---

Final Answers:

1. \(\boxed{148 \, \text{cm}^2, 68 \, \text{cm}}\)
2. \(\boxed{19 \, \text{in}^2, 32 \, \text{in}}\)
3. \(\boxed{198 \, \text{in}^2, 62 \, \text{in}}\)
4. \(\boxed{203.4 \, \text{ft}^2, 59.0 \, \text{ft}}\)
5. \(\boxed{174.42 \, \text{in}^2, 56.5 \, \text{in}}\)
6. \(\boxed{210.5 \, \text{ft}^2, 78.3 \, \text{ft}}\)
7. \(\boxed{207.4 \, \text{cm}^2, 66.7 \, \text{cm}}\)
8. \(\boxed{119.28 \, \text{m}^2, 46.8 \, \text{m}}\)