Step 1: Calculate the missing side lengths. The total height on the left is $3 \text{ cm}$. The inner vertical segment on the top-left is $2 \text{ cm}$. This means the vertical segment connecting the top-left inner corner to the bottom-left outer corner is $3 \text{ cm} - 2 \text{ cm} = 1 \text{ cm}$. The total width on the bottom is not directly given, but we can infer it from the segments. The bottom-right inner horizontal segment is $1 \text{ cm}$. The top-right horizontal segment is $3 \text{ cm}$. The top-left horizontal segment is $2 \text{ cm}$. The shape suggests that the total bottom width is the sum of the top-left horizontal segment and the bottom-right inner horizontal segment, plus the horizontal distance between them. However, looking at the diagram, it's more likely that the total bottom width is the sum of the top-left horizontal segment and the bottom-right inner horizontal segment, assuming the inner cut-out is aligned. Let's assume the total bottom width is $2 \text{ cm} + 1 \text{ cm} = 3 \text{ cm}$. Let's re-evaluate the shape. It appears to be a rectangle with a smaller rectangle removed from the bottom right corner. The outer dimensions of the large rectangle are: • Width: $2 \text{ cm} + 3 \text{ cm} = 5 \text{ cm}$ (sum of top horizontal segments) • Height: $3 \text{ cm}$ (left outer vertical segment) The dimensions of the removed rectangle are: • Width: $1 \text{ cm}$ (bottom-right inner horizontal segment) • Height: $1 \text{ cm}$ (bottom-right inner vertical segment) So, the sides of the shape are: • Top horizontal: $2 \text{ cm} + 3 \text{ cm} = 5 \text{ cm}$ • Right vertical: $3 \text{ cm}$ (outer edge) • Bottom horizontal: $5 \text{ cm}$ (outer edge) • Left vertical: $3 \text{ cm}$ (outer edge) However, there's an inner corner. The sides forming the inner corner are: • Vertical segment: $3 \text{ cm} - 1 \text{ cm} = 2 \text{ cm}$ (This is the segment from the top-left inner corner down to the inner bottom edge) • Horizontal segment: $5 \text{ cm} - 1 \text{ cm} = 4 \text{ cm}$ (This is the segment from the top-right inner corner left to the inner left edge) Let's trace the perimeter: 1. Top horizontal: $2 \text{ cm}$ 2. Top-right vertical: $3 \text{ cm} - 1 \text{ cm} = 2 \text{ cm}$ 3. Right horizontal: $3 \text{ cm} - 1 \text{ cm} = 2 \text{ cm}$ 4. Bottom horizontal: $1 \text{ cm}$ 5. Bottom-left vertical: $3 \text{ cm} - 2 \text{ cm} = 1 \text{ cm}$ 6. Left horizontal: $2 \text{ cm}$ Let's re-interpret the diagram based on the provided numbers. The outer rectangle has a height of $3 \text{ cm}$ and a width that appears to be $2 \text{ cm} + 3 \text{ cm} = 5 \text{ cm}$. A smaller rectangle is removed from the bottom right. The dimensions of the removed rectangle are $1 \text{ cm}$ (width) and $1 \text{ cm}$ (height). The sides of the shape are: • Top horizontal: $2 \text{ cm} + 3 \text{ cm} = 5 \text{ cm}$ • Right vertical (outer): $3 \text{ cm}$ • Bottom horizontal (outer): $5 \text{ cm}$ • Left vertical (outer): $3 \text{ cm}$ Now consider the inner corner. The vertical side of the inner corner is $3 \text{ cm} - 1 \text{ cm} = 2 \text{ cm}$. The horizontal side of the inner corner is $5 \text{ cm} - 1 \text{ cm} = 4 \text{ cm}$. Let's trace the perimeter again, starting from the top-left and going clockwise: 1. Top horizontal segment: $2 \text{ cm}$ 2. Top-right vertical segment: $3 \text{ cm} - 1 \text{ cm} = 2 \text{ cm}$ 3. Right horizontal segment: $3 \text{ cm} - 1 \text{ cm} = 2 \text{ cm}$ 4. Bottom horizontal segment: $1 \text{ cm}$ 5. Bottom-left vertical segment: $3 \text{ cm} - 2 \text{ cm} = 1 \text{ cm}$ 6. Left horizontal segment: $2 \text{ cm}$ This interpretation doesn't seem right. Let's assume the numbers given are the lengths of the segments as drawn. Perimeter calculation: • Top horizontal segment: $2 \text{ cm}$ • Vertical segment down from the $2 \text{ cm}$ mark: $2 \text{ cm}$ • Horizontal segment to the right: $3 \text{ cm}$ • Vertical segment down from the $3 \text{ cm}$ mark: $3 \text{ cm}$ • Horizontal segment to the left (inner): $1 \text{ cm}$ • Vertical segment up (inner): $1 \text{ cm}$ We need to find the lengths of the two remaining outer segments. The total height is $3 \text{ cm}$. The inner vertical segment is $1 \text{ cm}$. So the outer vertical segment on the right is $3 \text{ cm} - 1 \text{ cm} = 2 \text{ cm}$. The total width is $2 \text{ cm} + 3 \text{ cm} = 5 \text{ cm}$. The inner horizontal segment is $1 \text{ cm}$. So the outer horizontal segment on the bottom is $5 \text{ cm} - 1 \text{ cm} = 4 \text{ cm}$. Let's trace the perimeter again with these lengths: 1. Top horizontal: $2 \text{ cm}$ 2. Vertical segment: $2 \text{ cm}$ 3. Horizontal segment: $3 \text{ cm}$ 4. Outer right vertical: $2 \text{ cm}$ 5. Outer bottom horizontal: $4 \text{ cm}$ 6. Inner horizontal: $1 \text{ cm}$ 7. Inner vertical: $1 \text{ cm}$ 8. Left horizontal: $2 \text{ cm}$ This is still not adding up correctly. Let's assume the numbers are the lengths of the segments as they appear. Perimeter = Sum of all outer and inner boundary lengths. • Top horizontal: $2 \text{ cm}$ • Vertical segment: $2 \text{ cm}$ • Horizontal segment: $3 \text{ cm}$ • Outer right vertical segment: $3 \text{ cm}$ (This is the full height on the right) • Outer bottom horizontal segment: $2 \text{ cm} + 3 \text{ cm} = 5 \text{ cm}$ (This is the full width on the bottom) • Inner horizontal segment: $1 \text{ cm}$ • Inner vertical segment: $1 \text{ cm}$ This interpretation is also problematic. Let's assume the diagram represents a rectangle with a corner cut out. Outer rectangle dimensions: • Width = $2 \text{ cm} + 3 \text{ cm} = 5 \text{ cm}$ • Height = $3 \text{ cm}$ Cut-out rectangle dimensions: • Width = $1 \text{ cm}$ • Height = $1 \text{ cm}$ The perimeter consists of the outer boundary and the inner boundary. Outer boundary segments: • Top: $2 \text{ cm} + 3 \text{ cm} = 5 \text{ cm}$ • Right: $3 \text{ cm}$ • Bottom: $5 \text{ cm}$ • Left: $3 \text{ cm}$ Inner boundary segments (forming the cut-out): • Horizontal segment: $1 \text{ cm}$ • Vertical segment: $1 \text{ cm}$ This is not correct. The perimeter is the length of the boundary of the shape. Let's trace the boundary segments as labeled: 1. Top horizontal: $2 \text{ cm}$ 2. Vertical segment: $2 \text{ cm}$ 3. Horizontal segment: $3 \text{ cm}$ 4. Outer right vertical segment: $3 \text{ cm} - 1 \text{ cm} = 2 \text{ cm}$ 5. Outer bottom horizontal segment: $5 \text{ cm} - 1 \text{ cm} = 4 \text{ cm}$ 6. Inner horizontal segment: $1 \text{ cm}$ 7