Perimeter of compund shapes 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 perimeter includes:
- Two sides of the rectangle: \(14 \, \text{cm} + 14 \, \text{cm}\)
- One side of the rectangle: \(5 \, \text{cm}\)
- The hypotenuse of the triangle (which forms the slanted side).

2. To find the hypotenuse of the triangle:
\[
\text{Hypotenuse} = \sqrt{14^2 + 5^2} = \sqrt{196 + 25} = \sqrt{221} \approx 14.87 \, \text{cm}
\]

3. Total perimeter:
\[
\text{Perimeter} = 14 + 14 + 5 + 14.87 = 47.87 \, \text{cm}
\]

Answer for Shape 1:
\[
\boxed{47.87 \, \text{cm}}
\]

---

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 perimeter includes:
- The outer edges of the larger rectangle.
- The additional edges formed by the smaller rectangle.

2. Breakdown:
- Top edge: \(21 \, \text{cm}\)
- Bottom edge: \(20 \, \text{cm}\)
- Left edge: \(21 \, \text{cm}\)
- Right edge: \(20 \, \text{cm}\)
- Additional vertical edges from the smaller rectangle: \(11 \, \text{cm} + 10 \, \text{cm}\)
- Additional horizontal edge from the smaller rectangle: \(11 \, \text{cm}\)

3. Total perimeter:
\[
\text{Perimeter} = 21 + 20 + 21 + 20 + 11 + 10 + 11 = 114 \, \text{cm}
\]

Answer for Shape 2:
\[
\boxed{114 \, \text{cm}}
\]

---

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 perimeter includes:
- The outer edges of the larger rectangle.
- The additional edges formed by the smaller rectangle.

2. Breakdown:
- Top edge: \(19 \, \text{cm}\)
- Bottom edge: \(18 \, \text{cm}\)
- Left edge: \(19 \, \text{cm}\)
- Right edge: \(16 \, \text{cm}\)
- Additional horizontal edge from the smaller rectangle: \(16 \, \text{cm}\)
- Additional vertical edge from the smaller rectangle: \(16 \, \text{cm}\)

3. Total perimeter:
\[
\text{Perimeter} = 19 + 18 + 19 + 16 + 16 + 16 = 104 \, \text{cm}
\]

Answer for Shape 3:
\[
\boxed{104 \, \text{cm}}
\]

---

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 perimeter includes:
- The outer edges of the larger rectangle.
- The additional edges formed by the smaller rectangle.

2. Breakdown:
- Top edge: \(24 \, \text{m}\)
- Bottom edge: \(24 \, \text{m}\)
- Left edge: \(12 \, \text{m}\)
- Right edge: \(6 \, \text{m}\)
- Additional vertical edge from the smaller rectangle: \(2 \, \text{m}\)
- Additional horizontal edge from the smaller rectangle: \(10 \, \text{m}\)

3. Total perimeter:
\[
\text{Perimeter} = 24 + 24 + 12 + 6 + 2 + 10 = 78 \, \text{m}
\]

Answer for Shape 4:
\[
\boxed{78 \, \text{m}}
\]

---

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. The perimeter includes:
- All four sides of the trapezoid.

2. Total perimeter:
\[
\text{Perimeter} = 4 + 16 + 4 + 2 = 26 \, \text{m}
\]

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. The perimeter includes:
- All four sides of the trapezoid.

2. Total perimeter:
\[
\text{Perimeter} = 9 + 20 + 11 + 14 = 54 \, \text{m}
\]

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. The perimeter includes:
- All four sides of the shape.

2. Total perimeter:
\[
\text{Perimeter} = 12 + 16 + 14 + 5 = 47 \, \text{cm}
\]

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

---

Shape 8:

- The shape is a combination of three squares.
- Dimensions:
- Each square: \(36 \, \text{m} \times 36 \, \text{m}\)

#### Perimeter Calculation:
1. The perimeter includes:
- The outer edges of the combined shape.

2. Breakdown:
- Top edge: \(60 \, \text{m}\)
- Bottom edge: \(60 \, \text{m}\)
- Left edge: \(36 \, \text{m}\)
- Right edge: \(36 \, \text{m}\)
- Additional vertical edges: \(36 \, \text{m} + 36 \, \text{m}\)

3. Total perimeter:
\[
\text{Perimeter} = 60 + 60 + 36 + 36 + 36 + 36 = 264 \, \text{m}
\]

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

---

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 perimeter includes:
- The outer edges of the larger rectangle.
- The additional edges formed by the smaller rectangle.

2. Breakdown:
- Top edge: \(11 \, \text{m}\)
- Bottom edge: \(10 \, \text{m}\)
- Left edge: \(11 \, \text{m}\)
- Right edge: \(8 \, \text{m}\)
- Additional horizontal edge from the smaller rectangle: \(8 \, \text{m}\)
- Additional vertical edge from the smaller rectangle: \(8 \, \text{m}\)

3. Total perimeter:
\[
\text{Perimeter} = 11 + 10 + 11 + 8 + 8 + 8 = 56 \, \text{m}
\]

Answer for Shape 9:
\[
\boxed{56 \, \text{m}}
\]

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Final Answers:

1. \(\boxed{47.87 \, \text{cm}}\)
2. \(\boxed{114 \, \text{cm}}\)
3. \(\boxed{104 \, \text{cm}}\)
4. \(\boxed{78 \, \text{m}}\)
5. \(\boxed{26 \, \text{m}}\)
6. \(\boxed{54 \, \text{m}}\)
7. \(\boxed{47 \, \text{cm}}\)
8. \(\boxed{264 \, \text{m}}\)
9. \(\boxed{56 \, \text{m}}\)