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
Square perimeter: The distance around the square. Formula: P = 4 × side length
Side length = 6 cm
Perimeter = 4 × side length
P = 4 × 6
P = 24 cm
The perimeter of the square is 24 cm.
• Square perimeter formula: P = 4 × side length
• All sides equal: In a square, all four sides are the same length
• Units: Always include units in the final answer
Combined shape perimeter: Add the perimeters of individual parts, excluding shared sides.
Rectangle perimeter = 2 × (length + width)
P = 2 × (10 + 4) = 2 × 14 = 28 cm
Square perimeter = 4 × side length
P = 4 × 4 = 16 cm
Don't count the shared side (width of rectangle where square is attached)
Total perimeter = Rectangle P + Square P - 2 × shared side
P = 28 + 16 - 2×4 = 44 - 8 = 36 cm
The perimeter of the combined shape is 36 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
Square perimeter: The distance around the square. Formula: P = 4 × side length
Side length = 9 cm
Perimeter = 4 × side length
P = 4 × 9
P = 36 cm
The perimeter of the square is 36 cm.
• Square perimeter formula: P = 4 × side length
• All sides equal: In a square, all four sides are the same length
• Units: Always include units in the final answer
Combined shape perimeter: Add the perimeters of individual parts, excluding shared sides.
Rectangle perimeter = 2 × (length + width)
P = 2 × (15 + 5) = 2 × 20 = 40 cm
Square perimeter = 4 × side length
P = 4 × 5 = 20 cm
Don't count the shared side (width of rectangle where square is attached)
Total perimeter = Rectangle P + Square P - 2 × shared side
P = 40 + 20 - 2×5 = 60 - 10 = 50 cm
The perimeter of the combined shape is 50 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 = 20 cm, Width = 10 cm
Perimeter = 2 × (length + width)
P = 2 × (20 + 10)
P = 2 × 30 = 60 cm
The perimeter of the rectangle is 60 cm.
• Perimeter formula: P = 2 × (length + width)
• Order of operations: Calculate parentheses first
• Units: Always include units in the final answer
Square perimeter: The distance around the square. Formula: P = 4 × side length
Side length = 12 cm
Perimeter = 4 × side length
P = 4 × 12
P = 48 cm
The perimeter of the square is 48 cm.
• Square perimeter formula: P = 4 × side length
• All sides equal: In a square, all four sides are the same length
• Units: Always include units in the final answer
Combined shape perimeter: Add the perimeters of individual parts, excluding shared sides.
Rectangle perimeter = 2 × (length + width)
P = 2 × (18 + 6) = 2 × 24 = 48 cm
Square perimeter = 4 × side length
P = 4 × 6 = 24 cm
Don't count the shared side (width of rectangle where square is attached)
Total perimeter = Rectangle P + Square P - 2 × shared side
P = 48 + 24 - 2×6 = 72 - 12 = 60 cm
The perimeter of the combined shape is 60 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 squares are added to opposite sides of a rectangle, the straight sides cancel out.
Rectangle perimeter = 2 × (length + width)
P = 2 × (14 + 8) = 2 × 22 = 44 cm
Each square has side length = 8 cm
Perimeter of two squares = 2 × 4 × 8 = 64 cm
Don't count the shared sides (both widths of rectangle where squares are attached)
Total perimeter = Rectangle P + 2×Square P - 4×shared side
P = 44 + 64 - 4×8 = 108 - 32 = 76 cm
The perimeter of the advanced combined shape is 76 cm.
• Shared sides: Don't count sides shared between shapes
• Multiple attachments: Account for all shared sides
• 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
Square: A four-sided shape with four right angles and all sides equal
- Identify the shape(s): Determine if rectangle, square, or combination
- Select the formula: Rectangle: P = 2(l + w), Square: P = 4s
- Apply the formula: Substitute known values
- Calculate: Perform the arithmetic
- Check units: Include appropriate measurement units
• Rectangle perimeter: P = 2(length + width)
• Square perimeter: P = 4 × side length
• Alternative rectangle: P = length + width + length + width
• Square as rectangle: P = 2(side + side) = 2(2s) = 4s
Questions & Answers
Question: Why do we multiply by 2 in the rectangle perimeter formula?
Answer: Great question! A rectangle has two pairs of equal sides:
- Two sides with length = length
- Two sides with length = width
So the total perimeter is: length + width + length + width
We can group these: (length + length) + (width + width) = 2×length + 2×width
Using the distributive property: 2×length + 2×width = 2×(length + width)
That's why the formula is P = 2(l + w) - it's just a shorter way to add all four sides!
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 square) 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 square is attached to a rectangle, the side of the rectangle where the square attaches becomes internal. So you calculate the rectangle perimeter, add the square perimeter, then subtract the lengths of the shared sides.
Drawing the shape and tracing the outer path can help visualize which sides to include.
Question: Is a square just a special kind of rectangle?
Answer: Yes, absolutely! A square is a special type of rectangle where all four sides are equal in length. This means:
- A square has all the properties of a rectangle (four right angles, opposite sides equal)
- Plus the additional property that all four sides are equal
- You can use the rectangle formula for a square: P = 2(l + w) where l = w = s
- This gives: P = 2(s + s) = 2(2s) = 4s
So the square perimeter formula P = 4s is really just the rectangle formula with the special condition that length = width.
Think of it this way: All squares are rectangles, but not all rectangles are squares!
Visual Guide: Perimeter of Rectangle and Square
Complete Summary: Perimeter of Rectangle and Square
Perimeter: The total distance around the outside of a shape.
Rectangle: A four-sided shape with four right angles (90°), opposite sides are equal and parallel.
Square: A four-sided shape with four right angles and all four sides equal in length.
Dimensions: Length (longer side) and width (shorter side) for rectangles; side length for squares.
Rectangle Perimeter: P = 2(l + w) or P = l + w + l + w
Square Perimeter: P = 4s or P = s + s + s + s
Special Relationship: A square is a special rectangle where length = width = s
Alternative Calculation: Add all side lengths individually
- Identify the Shape: Determine if rectangle, square, or combination
- Measure Dimensions: Find length, width, or side length
- Select Formula: Choose appropriate perimeter formula
- Substitute Values: Replace variables with actual measurements
- Calculate: Perform the mathematical operations
- Include Units: Always add measurement units (cm, m, in, ft, etc.)
Simple Rectangle: Length = 5 cm, Width = 3 cm
P = 2(5 + 3) = 2(8) = 16 cm
Simple Square: Side = 7 cm
P = 4 × 7 = 28 cm
Combined Shape: Rectangle (8×4) + Square (side 4)
P = 2(8+4) + 4×4 - 2×4 = 24 + 16 - 8 = 32 cm
- Memorization Trick: "2 times length plus width" for rectangles
- Four Sides: Remember squares have 4 equal sides
- Unit Consistency: All measurements must be in the same unit
- Common Mistake: Forgetting to multiply by 2 in rectangle formula
- Shared Sides: Don't count sides shared between shapes twice
- Verification: Add all sides individually to check your answer
- Rectangles: Opposite sides equal, P = 2(length + width)
- Squares: All sides equal, P = 4 × side length
- Connection: Square is a special rectangle (l = w)
- Perimeter: Always measures the outside boundary
- Practice: Work with various dimensions to build fluency
- Visualization: Draw shapes to understand shared sides