Perimeter of irregular polygons worksheet - Free Printable

To solve the problem of finding the perimeter of each compound shape, we need to calculate the total length of all the outer edges of each figure. Let's go through each shape step by step.

---

Shape 1:

- The shape is a combination of a rectangle and a triangle.
- Dimensions:
- Rectangle: \(14 \, \text{cm} \times 5 \, \text{cm}\)
- Triangle: Base = \(14 \, \text{cm}\), Height = \(5 \, \text{cm}\)

#### Perimeter Calculation:
1. The two longer sides of the rectangle are \(14 \, \text{cm}\) each.
2. The shorter side of the rectangle is \(5 \, \text{cm}\).
3. The hypotenuse of the triangle can be calculated using the Pythagorean theorem:
\[
\text{Hypotenuse} = \sqrt{14^2 + 5^2} = \sqrt{196 + 25} = \sqrt{221} \approx 14.87 \, \text{cm}
\]
4. The other side of the triangle is already given as \(5 \, \text{cm}\).

#### Total Perimeter:
\[
14 + 14 + 5 + 5 + 14.87 = 52.87 \, \text{cm}
\]

Answer for Shape 1:
\[
\boxed{52.87 \, \text{cm}}
\]

---

Shape 2:

- The shape is a combination of two rectangles.
- Dimensions:
- Larger rectangle: \(21 \, \text{cm} \times 20 \, \text{cm}\)
- Smaller rectangle: \(11 \, \text{cm} \times 10 \, \text{cm}\)

#### Perimeter Calculation:
1. The outer dimensions of the larger rectangle are \(21 \, \text{cm}\) and \(20 \, \text{cm}\).
2. The smaller rectangle adds an additional \(11 \, \text{cm}\) and \(10 \, \text{cm}\) to the perimeter, but some sides overlap.

#### Total Perimeter:
- Top: \(21 \, \text{cm}\)
- Bottom: \(20 \, \text{cm}\)
- Left side: \(21 \, \text{cm}\)
- Right side: \(20 \, \text{cm}\)
- Additional vertical side from the smaller rectangle: \(11 \, \text{cm}\)
- Additional horizontal side from the smaller rectangle: \(10 \, \text{cm}\)

\[
21 + 20 + 21 + 20 + 11 + 10 = 103 \, \text{cm}
\]

Answer for Shape 2:
\[
\boxed{103 \, \text{cm}}
\]

---

Shape 3:

- The shape is a combination of two rectangles.
- Dimensions:
- Larger rectangle: \(19 \, \text{cm} \times 18 \, \text{cm}\)
- Smaller rectangle: \(16 \, \text{cm} \times 16 \, \text{cm}\)

#### Perimeter Calculation:
1. The outer dimensions of the larger rectangle are \(19 \, \text{cm}\) and \(18 \, \text{cm}\).
2. The smaller rectangle adds an additional \(16 \, \text{cm}\) and \(16 \, \text{cm}\) to the perimeter, but some sides overlap.

#### Total Perimeter:
- Top: \(19 \, \text{cm}\)
- Bottom: \(18 \, \text{cm}\)
- Left side: \(19 \, \text{cm}\)
- Right side: \(18 \, \text{cm}\)
- Additional vertical side from the smaller rectangle: \(16 \, \text{cm}\)
- Additional horizontal side from the smaller rectangle: \(16 \, \text{cm}\)

\[
19 + 18 + 19 + 18 + 16 + 16 = 106 \, \text{cm}
\]

Answer for Shape 3:
\[
\boxed{106 \, \text{cm}}
\]

---

Shape 4:

- The shape is a combination of two rectangles.
- Dimensions:
- Larger rectangle: \(24 \, \text{m} \times 12 \, \text{m}\)
- Smaller rectangle: \(10 \, \text{m} \times 6 \, \text{m}\)

#### Perimeter Calculation:
1. The outer dimensions of the larger rectangle are \(24 \, \text{m}\) and \(12 \, \text{m}\).
2. The smaller rectangle adds an additional \(10 \, \text{m}\) and \(6 \, \text{m}\) to the perimeter, but some sides overlap.

#### Total Perimeter:
- Top: \(24 \, \text{m}\)
- Bottom: \(12 \, \text{m}\)
- Left side: \(24 \, \text{m}\)
- Right side: \(12 \, \text{m}\)
- Additional vertical side from the smaller rectangle: \(10 \, \text{m}\)
- Additional horizontal side from the smaller rectangle: \(6 \, \text{m}\)

\[
24 + 12 + 24 + 12 + 10 + 6 = 88 \, \text{m}
\]

Answer for Shape 4:
\[
\boxed{88 \, \text{m}}
\]

---

Shape 5:

- The shape is a trapezoid.
- Dimensions:
- Top base: \(4 \, \text{m}\)
- Bottom base: \(16 \, \text{m}\)
- Left side: \(4 \, \text{m}\)
- Right side: \(2 \, \text{m}\)

#### Perimeter Calculation:
1. Add all the sides together.

\[
4 + 16 + 4 + 2 = 26 \, \text{m}
\]

Answer for Shape 5:
\[
\boxed{26 \, \text{m}}
\]

---

Shape 6:

- The shape is a trapezoid.
- Dimensions:
- Top base: \(9 \, \text{m}\)
- Bottom base: \(20 \, \text{m}\)
- Left side: \(11 \, \text{m}\)
- Right side: \(14 \, \text{m}\)

#### Perimeter Calculation:
1. Add all the sides together.

\[
9 + 20 + 11 + 14 = 54 \, \text{m}
\]

Answer for Shape 6:
\[
\boxed{54 \, \text{m}}
\]

---

Shape 7:

- The shape is a triangle.
- Dimensions:
- Sides: \(12 \, \text{cm}\), \(16 \, \text{cm}\), \(14 \, \text{cm}\), and \(5 \, \text{cm}\)

#### Perimeter Calculation:
1. Add all the sides together.

\[
12 + 16 + 14 + 5 = 47 \, \text{cm}
\]

Answer for Shape 7:
\[
\boxed{47 \, \text{cm}}
\]

---

Shape 8:

- The shape is a combination of two rectangles.
- Dimensions:
- Larger rectangle: \(60 \, \text{m} \times 36 \, \text{m}\)
- Smaller rectangle: \(36 \, \text{m} \times 36 \, \text{m}\)

#### Perimeter Calculation:
1. The outer dimensions of the larger rectangle are \(60 \, \text{m}\) and \(36 \, \text{m}\).
2. The smaller rectangle adds an additional \(36 \, \text{m}\) and \(36 \, \text{m}\) to the perimeter, but some sides overlap.

#### Total Perimeter:
- Top: \(60 \, \text{m}\)
- Bottom: \(36 \, \text{m}\)
- Left side: \(60 \, \text{m}\)
- Right side: \(36 \, \text{m}\)
- Additional vertical side from the smaller rectangle: \(36 \, \text{m}\)
- Additional horizontal side from the smaller rectangle: \(36 \, \text{m}\)

\[
60 + 36 + 60 + 36 + 36 + 36 = 264 \, \text{m}
\]

Answer for Shape 8:
\[
\boxed{264 \, \text{m}}
\]

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Shape 9:

- The shape is a combination of two rectangles.
- Dimensions:
- Larger rectangle: \(11 \, \text{m} \times 10 \, \text{m}\)
- Smaller rectangle: \(8 \, \text{m} \times 8 \, \text{m}\)

#### Perimeter Calculation:
1. The outer dimensions of the larger rectangle are \(11 \, \text{m}\) and \(10 \, \text{m}\).
2. The smaller rectangle adds an additional \(8 \, \text{m}\) and \(8 \, \text{m}\) to the perimeter, but some sides overlap.

#### Total Perimeter:
- Top: \(11 \, \text{m}\)
- Bottom: \(10 \, \text{m}\)
- Left side: \(11 \, \text{m}\)
- Right side: \(10 \, \text{m}\)
- Additional vertical side from the smaller rectangle: \(8 \, \text{m}\)
- Additional horizontal side from the smaller rectangle: \(8 \, \text{m}\)

\[
11 + 10 + 11 + 10 + 8 + 8 = 58 \, \text{m}
\]

Answer for Shape 9:
\[
\boxed{58 \, \text{m}}
\]

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Final Answers:

1. \( \boxed{52.87 \, \text{cm}} \)
2. \( \boxed{103 \, \text{cm}} \)
3. \( \boxed{106 \, \text{cm}} \)
4. \( \boxed{88 \, \text{m}} \)
5. \( \boxed{26 \, \text{m}} \)
6. \( \boxed{54 \, \text{m}} \)
7. \( \boxed{47 \, \text{cm}} \)
8. \( \boxed{264 \, \text{m}} \)
9. \( \boxed{58 \, \text{m}} \)