Rectangle perimeter: The distance around the rectangle. Formula: P = 2 × (length + width)
- Add the length and width
- Multiply the sum by 2
- State the unit (cm, m, etc.)
Length = 8 cm, Width = 5 cm
Perimeter = 2 × (length + width)
P = 2 × (8 + 5)
P = 2 × 13 = 26 cm
The perimeter of the rectangle is 26 cm.
• Perimeter formula: P = 2 × (length + width)
• Order of operations: Calculate parentheses first
• Units: Always include units in the final answer
Semicircle perimeter: The distance around the curved edge. Formula: P = π × r (where r is radius)
Radius = Diameter ÷ 2 = 10 ÷ 2 = 5 cm
Perimeter of semicircle = π × radius
P = π × 5
P = 3.14 × 5 = 15.7 cm
The perimeter of the semicircle is approximately 15.7 cm.
• Radius relationship: Radius = Diameter ÷ 2
• Semicircle perimeter: P = π × r
• Value of π: Use 3.14 for approximation
Combined shape perimeter: Add the perimeters of individual parts, excluding shared sides.
Rectangle perimeter = 2 × (length + width)
P = 2 × (6 + 4) = 2 × 10 = 20 cm
Since diameter = 4 cm, radius = 2 cm
Semicircle perimeter = π × radius = 3.14 × 2 = 6.28 cm
Don't count the shared side (width of rectangle where semicircle is attached)
Total perimeter = Rectangle P - width + Semicircle P
P = 20 - 4 + 6.28 = 24.28 cm
The perimeter of the combined shape is approximately 24.28 cm.
• Shared sides: Don't count sides shared between shapes
• Individual calculations: Calculate each shape separately first
• Addition principle: Add individual perimeters after removing shared parts
Rectangle perimeter: The distance around the rectangle. Formula: P = 2 × (length + width)
Length = 12 cm, Width = 7 cm
Perimeter = 2 × (length + width)
P = 2 × (12 + 7)
P = 2 × 19 = 38 cm
The perimeter of the rectangle is 38 cm.
• Perimeter formula: P = 2 × (length + width)
• Order of operations: Calculate parentheses first
• Units: Always include units in the final answer
Semicircle perimeter: The distance around the curved edge. Formula: P = π × r (where r is radius)
Radius = Diameter ÷ 2 = 14 ÷ 2 = 7 cm
Perimeter of semicircle = π × radius
P = π × 7
P = 3.14 × 7 = 21.98 cm
The perimeter of the semicircle is approximately 21.98 cm.
• Radius relationship: Radius = Diameter ÷ 2
• Semicircle perimeter: P = π × r
• Value of π: Use 3.14 for approximation
Combined shape perimeter: Add the perimeters of individual parts, excluding shared sides.
Rectangle perimeter = 2 × (length + width)
P = 2 × (10 + 6) = 2 × 16 = 32 cm
Since diameter = 6 cm, radius = 3 cm
Semicircle perimeter = π × radius = 3.14 × 3 = 9.42 cm
Don't count the shared side (width of rectangle where semicircle is attached)
Total perimeter = Rectangle P - width + Semicircle P
P = 32 - 6 + 9.42 = 35.42 cm
The perimeter of the combined shape is approximately 35.42 cm.
• Shared sides: Don't count sides shared between shapes
• Individual calculations: Calculate each shape separately first
• Addition principle: Add individual perimeters after removing shared parts
Rectangle perimeter: The distance around the rectangle. Formula: P = 2 × (length + width)
Length = 15 cm, Width = 9 cm
Perimeter = 2 × (length + width)
P = 2 × (15 + 9)
P = 2 × 24 = 48 cm
The perimeter of the rectangle is 48 cm.
• Perimeter formula: P = 2 × (length + width)
• Order of operations: Calculate parentheses first
• Units: Always include units in the final answer
Semicircle perimeter: The distance around the curved edge. Formula: P = π × r (where r is radius)
Radius = Diameter ÷ 2 = 16 ÷ 2 = 8 cm
Perimeter of semicircle = π × radius
P = π × 8
P = 3.14 × 8 = 25.12 cm
The perimeter of the semicircle is approximately 25.12 cm.
• Radius relationship: Radius = Diameter ÷ 2
• Semicircle perimeter: P = π × r
• Value of π: Use 3.14 for approximation
Combined shape perimeter: Add the perimeters of individual parts, excluding shared sides.
Rectangle perimeter = 2 × (length + width)
P = 2 × (8 + 5) = 2 × 13 = 26 cm
Since diameter = 5 cm, radius = 2.5 cm
Semicircle perimeter = π × radius = 3.14 × 2.5 = 7.85 cm
Don't count the shared side (width of rectangle where semicircle is attached)
Total perimeter = Rectangle P - width + Semicircle P
P = 26 - 5 + 7.85 = 28.85 cm
The perimeter of the combined shape is approximately 28.85 cm.
• Shared sides: Don't count sides shared between shapes
• Individual calculations: Calculate each shape separately first
• Addition principle: Add individual perimeters after removing shared parts
Advanced combined shape perimeter: Add the perimeters of individual parts, excluding shared sides. When two semicircles are added to opposite sides of a rectangle, the straight sides cancel out.
Rectangle perimeter = 2 × (length + width)
P = 2 × (12 + 8) = 2 × 20 = 40 cm
Each semicircle has diameter = 8 cm, so radius = 4 cm
Two semicircles = one full circle
Perimeter of two semicircles = 2 × π × radius = 2 × 3.14 × 4 = 25.12 cm
Don't count the shared sides (both widths of rectangle where semicircles are attached)
Total perimeter = Rectangle P - 2×width + 2×Semicircle P
P = 40 - 16 + 25.12 = 49.12 cm
The perimeter of the advanced combined shape is approximately 49.12 cm.
• Shared sides: Don't count sides shared between shapes
• Two semicircles: Equal to one full circle
• Complex combinations: Carefully track which sides to exclude
Perimeter: The distance around the outside of a shape
Rectangle: A four-sided shape with four right angles
Semicircle: Half of a circle
- Identify the shape(s): Determine if rectangle, semicircle, or combination
- Select the formula: Rectangle: P = 2(l + w), Semicircle: P = πr
- Apply the formula: Substitute known values
- Calculate: Perform the arithmetic
- Check units: Include appropriate measurement units
• Rectangle perimeter: P = 2(length + width)
• Semicircle perimeter: P = π × radius
• Circle circumference: C = 2π × radius
• Radius = Diameter ÷ 2
• Diameter = Radius × 2
Questions & Answers
Question: Why is the perimeter of a semicircle πr and not πr + d? Shouldn't we include the diameter too?
Answer: Great question! The answer depends on the context:
- When calculating just the curved edge of a semicircle, the perimeter is indeed just πr.
- When calculating the total perimeter of a semicircle shape (including the straight edge), it would be πr + d (or πr + 2r).
In our exercises, we focused on the curved edge of the semicircle, which is why the formula is P = πr. This is specifically the arc length of the semicircle.
If you were finding the perimeter of a semicircle as a standalone shape (not attached to anything), you would include the diameter: P = πr + 2r. But when it's part of a combined shape, we typically only count the curved edge.
Question: How do I know which sides to subtract when combining shapes?
Answer: The key is to identify which sides are internal to the combined shape:
- Count only the outer edges of the combined shape
- Sides that are inside the shape (shared between the rectangle and semicircle) should not be counted
- Visualize walking around the outside of the shape - only count the distances you walk along the outside
For example, when a semicircle is attached to a rectangle, the width of the rectangle where the semicircle attaches becomes internal. So you calculate the rectangle perimeter but subtract that width, then add the semicircle's curved edge.
Drawing the shape and tracing the outer path can help visualize which sides to include.
Question: What happens to the perimeter when two semicircles are attached to opposite sides of a rectangle?
Answer: When two semicircles of equal diameter are attached to opposite sides of a rectangle, something interesting happens:
- The two semicircles together form a complete circle
- You subtract both widths of the rectangle (where the semicircles attach) from the rectangle's perimeter
- You add the circumference of the full circle (which is the two semicircles combined)
So for a rectangle with length L and width W, with semicircles of diameter W on both ends:
Total perimeter = 2L + 2W - 2W + πW = 2L + πW
This creates a shape that looks like a racetrack, and the perimeter consists of the two lengths of the rectangle plus the circumference of the circle formed by the two semicircles.