Perimeter of irregular shapes worksheet - Free Printable

Problem Analysis:

We are tasked with finding the missing side lengths marked as \( x \) or \( y \) in two irregular shapes and then calculating the perimeter of each shape.

---

Shape 1:

#### Step 1: Identify the given dimensions.
- The shape is composed of rectangles.
- Dimensions provided:
- Bottom side: 15 cm
- Left vertical side: 11 cm
- Right vertical side: 9 cm
- Top horizontal segment: 9 cm

#### Step 2: Determine the missing side \( x \).
- The total length of the bottom side is 15 cm.
- The top horizontal segment is 9 cm.
- The remaining part of the bottom side (which is \( x \)) can be calculated as:
\[
x = 15 \, \text{cm} - 9 \, \text{cm} = 6 \, \text{cm}
\]

#### Step 3: Calculate the perimeter.
- Perimeter is the sum of all the outer sides.
- The sides are:
- Bottom: 15 cm
- Left vertical: 11 cm
- Right vertical: 9 cm
- Top horizontal segments: 9 cm + 6 cm (from \( x \))
- Summing these:
\[
\text{Perimeter} = 15 + 11 + 9 + 9 + 6 = 50 \, \text{cm}
\]

#### Final Answers for Shape 1:
\[
\boxed{6 \, \text{cm}, 50 \, \text{cm}}
\]

---

Shape 2:

#### Step 1: Identify the given dimensions.
- The shape is composed of rectangles.
- Dimensions provided:
- Left vertical side: 15 mm
- Top horizontal segment: 6 mm
- Middle vertical segment: 9 mm
- Bottom horizontal segment: 14 mm
- Right vertical segment: 6 mm

#### Step 2: Determine the missing side \( x \).
- The total height of the shape is the sum of the vertical segments:
\[
\text{Total height} = 15 \, \text{mm} + 9 \, \text{mm} = 24 \, \text{mm}
\]
- The right vertical segment is given as 6 mm.
- The missing vertical segment \( x \) can be calculated as:
\[
x = 24 \, \text{mm} - 6 \, \text{mm} = 18 \, \text{mm}
\]

#### Step 3: Calculate the perimeter.
- Perimeter is the sum of all the outer sides.
- The sides are:
- Left vertical: 15 mm
- Top horizontal: 6 mm
- Middle vertical: 9 mm
- Bottom horizontal: 14 mm
- Right vertical: 6 mm
- Missing vertical segment: 18 mm
- Summing these:
\[
\text{Perimeter} = 15 + 6 + 9 + 14 + 6 + 18 = 68 \, \text{mm}
\]

#### Final Answers for Shape 2:
\[
\boxed{18 \, \text{mm}, 68 \, \text{mm}}
\]

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Final Summary:

1. For Shape 1:
- \( x = 6 \, \text{cm} \)
- Perimeter = \( 50 \, \text{cm} \)

2. For Shape 2:
- \( x = 18 \, \text{mm} \)
- Perimeter = \( 68 \, \text{mm} \)

\[
\boxed{6 \, \text{cm}, 50 \, \text{cm}, 18 \, \text{mm}, 68 \, \text{mm}}
\]