Perimeter of a Composite Figure worksheet - Free Printable

Problem: Calculate the perimeter of each composite figure.

#### Steps to Success:
1. Read and highlight the given information.
2. Observe the diagram and count & label the number of sides.
3. Find the missing side(s).
4. Write the formula for the perimeter: \( P = \text{Sum of All Sides} \).
5. Check to ensure all sides are added correctly.

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Figure 1:

#### Given:
- Dimensions: 8 cm, 10 cm, 7 cm, 5 cm, 3 cm
- Missing side: The horizontal segment at the bottom.

#### Solution:
1. Identify the missing side:
- The total length of the top horizontal segment is 8 cm.
- The two vertical segments on the left are 3 cm and 7 cm, respectively.
- The bottom horizontal segment is split into two parts: one labeled as 5 cm and the other as the missing side.
- To find the missing side, subtract the known horizontal segments from the total length:
\[
\text{Missing side} = 8 \, \text{cm} - 5 \, \text{cm} = 3 \, \text{cm}
\]

2. Calculate the perimeter:
- Sum all the sides:
\[
P = 8 \, \text{cm} + 10 \, \text{cm} + 7 \, \text{cm} + 5 \, \text{cm} + 3 \, \text{cm} + 3 \, \text{cm}
\]
\[
P = 36 \, \text{cm}
\]

#### Answer for Figure 1:
\[
\boxed{36}
\]

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Figure 2:

#### Given:
- Dimensions: 12 cm, 9 cm, 7 cm, 8 cm
- Missing side: The horizontal segment at the bottom.

#### Solution:
1. Identify the missing side:
- The total length of the top horizontal segment is 12 cm.
- The bottom horizontal segment is split into two parts: one labeled as 8 cm and the other as the missing side.
- To find the missing side, subtract the known horizontal segments from the total length:
\[
\text{Missing side} = 12 \, \text{cm} - 8 \, \text{cm} = 4 \, \text{cm}
\]

2. Calculate the perimeter:
- Sum all the sides:
\[
P = 12 \, \text{cm} + 9 \, \text{cm} + 7 \, \text{cm} + 8 \, \text{cm} + 4 \, \text{cm}
\]
\[
P = 40 \, \text{cm}
\]

#### Answer for Figure 2:
\[
\boxed{40}
\]

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Figure 3:

#### Given:
- Dimensions: 60 mm, 15 mm, 40 mm, 30 mm
- Missing side: The vertical segment on the right.

#### Solution:
1. Identify the missing side:
- The total height of the shape is the sum of the two vertical segments on the left: \( 15 \, \text{mm} + 30 \, \text{mm} = 45 \, \text{mm} \).
- The vertical segment on the right is the missing side, which must be equal to the total height:
\[
\text{Missing side} = 45 \, \text{mm}
\]

2. Calculate the perimeter:
- Sum all the sides:
\[
P = 60 \, \text{mm} + 15 \, \text{mm} + 40 \, \text{mm} + 30 \, \text{mm} + 45 \, \text{mm}
\]
\[
P = 190 \, \text{mm}
\]

#### Answer for Figure 3:
\[
\boxed{190}
\]

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Figure 4:

#### Given:
- Dimensions: 7½ m, 4 m, 2 m, 1½ m
- Missing side: The horizontal segment at the bottom.

#### Solution:
1. Identify the missing side:
- The total length of the top horizontal segment is 7½ m.
- The bottom horizontal segment is split into two parts: one labeled as 2 m and the other as the missing side.
- To find the missing side, subtract the known horizontal segments from the total length:
\[
\text{Missing side} = 7.5 \, \text{m} - 2 \, \text{m} = 5.5 \, \text{m}
\]

2. Calculate the perimeter:
- Sum all the sides:
\[
P = 7.5 \, \text{m} + 4 \, \text{m} + 1.5 \, \text{m} + 2 \, \text{m} + 5.5 \, \text{m}
\]
\[
P = 20.5 \, \text{m}
\]

#### Answer for Figure 4:
\[
\boxed{20.5}
\]

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Final Answers:

1. \( \boxed{36} \)
2. \( \boxed{40} \)
3. \( \boxed{190} \)
4. \( \boxed{20.5} \)