Printable Perimeter Word Problems for Grade 4

Comprehensive PDF worksheets: rectangles, squares, triangles, and complex shapes with detailed solutions.

PDF Worksheet Solutions: Exercises 1 to 3
1 Rectangle with missing dimension
Exercise 1
A rectangular playground has a width of 12 meters and a perimeter of 40 meters. What is the length of the playground? Create a labeled diagram showing the dimensions.
Definition:

Perimeter Formula Rearrangement: If P = 2(l + w), then l = (P/2) - w. This is essential for PDF worksheet problems.

PDF Worksheet Method:
  1. Read the problem carefully and identify known values
  2. Write the appropriate perimeter formula
  3. Substitute known values and rearrange to solve for unknown
  4. Create a labeled diagram for visual representation
  5. Verify the solution and include units
Given
P = 40m, w = 12m
Formula
l = (P/2) - w
Result
l = 8m
Step 1: Identify known values

Perimeter = 40 meters, Width = 12 meters, Length = ?

Step 2: Write the perimeter formula

Perimeter = 2 × (length + width)

40 = 2 × (length + 12)

Step 3: Divide both sides by 2

40 ÷ 2 = length + 12

20 = length + 12

Step 4: Subtract 12 from both sides

20 - 12 = length

8 = length

Step 5: Verify and create diagram

Check: 2 × (8 + 12) = 2 × 20 = 40 ✓

The length of the playground is 8 meters
Final answer:

The length of the rectangular playground is 8 meters. Diagram: Rectangle with length = 8m and width = 12m.

Applied rules:

• Perimeter Formula: P = 2(length + width)

• Algebraic Manipulation: Rearrange to solve for unknown

• Verification: Always check your answer in PDF worksheets

2 Multiple shapes comparison
Exercise 2
A square garden has sides of 10 feet. A rectangular garden has a length of 15 feet and a width of 5 feet. Which garden has a larger perimeter? Show your work with formulas and calculations.
Definition:

Comparison Problems: Calculate each shape's perimeter using appropriate formulas and compare results. Essential for PDF worksheet completion.

Square
P = 4 × 10 = 40ft
Rectangle
P = 2(15+5) = 40ft
Comparison
Equal perimeters
Step 1: Calculate the square's perimeter

Square: P = 4 × side = 4 × 10 = 40 feet

Formula: P = 4s

Step 2: Calculate the rectangle's perimeter

Rectangle: P = 2 × (length + width) = 2 × (15 + 5) = 2 × 20 = 40 feet

Formula: P = 2(l + w)

Step 3: Compare the perimeters

Square perimeter: 40 feet, Rectangle perimeter: 40 feet

Both gardens have the same perimeter

Step 4: Present findings for PDF

Show all work clearly with formulas and calculations

Step 5: State the conclusion

Both gardens have equal perimeters of 40 feet

Both gardens have the same perimeter of 40 feet
Final answer:

Both gardens have the same perimeter of 40 feet. Square: P = 4×10 = 40ft. Rectangle: P = 2×(15+5) = 40ft.

Applied rules:

• Square Perimeter: P = 4 × side

• Rectangle Perimeter: P = 2(length + width)

• PDF Format: Show all formulas and calculations clearly

3 Triangle with equal sides
Exercise 3
An equilateral triangle has a perimeter of 36 centimeters. What is the length of each side? Draw the triangle and label all sides with the calculated measurement.
Definition:

Equilateral Triangle: A triangle with all three sides equal. P = 3 × side. Perfect for PDF worksheet practice.

Given
P = 36cm
Formula
s = P ÷ 3
Result
s = 12cm
Step 1: Identify the triangle type

Equilateral triangle: all three sides are equal

Step 2: Write the perimeter formula

Perimeter = side + side + side = 3 × side

36 = 3 × side

Step 3: Solve for the side length

Side = 36 ÷ 3 = 12 centimeters

Step 4: Verify the answer

Check: 12 + 12 + 12 = 36 ✓

Step 5: Create diagram for PDF

Draw equilateral triangle with all sides labeled as 12cm

Each side of the triangle is 12 centimeters
Final answer:

Each side of the equilateral triangle is 12 centimeters long. All three sides measure 12cm.

Applied rules:

• Equilateral Triangle: P = 3 × side

• Division: To find one side, divide perimeter by 3

• PDF Visualization: Include diagrams with proper labeling

PDF Worksheet Formulas & Methods
Rectangle: \(P = 2(l + w)\)
Rectangle Perimeter
Square
\(P = 4s\)
Perimeter of Square
Triangle
\(P = a + b + c\)
Perimeter of Triangle
Equilateral Triangle
\(P = 3s\)
Special Case
Key definitions:

Perimeter: The distance around the outside of a shape

Rectangle: A 4-sided shape with 4 right angles and opposite sides equal

Square: A rectangle with all 4 sides equal

Equilateral Triangle: A triangle with all 3 sides equal

PDF Worksheet: Structured practice materials for organized learning

PDF Worksheet methodology:
  1. Read carefully: Understand what the problem is asking
  2. Identify shapes: Determine which geometric shapes are involved
  3. Select formulas: Use the appropriate perimeter formula
  4. Show work: Write down all calculations and formulas used
  5. Include diagrams: Draw shapes when requested
  6. Check answers: Verify solutions before completing PDF
Tip 1: Always show your work in PDF worksheets - teachers need to see your thinking process.
Tip 2: Draw diagrams neatly with rulers for better visualization in PDF format.
Tip 3: Write formulas clearly before substituting values in PDF worksheets.
Tip 4: Always include units in your final answers for PDF submissions.
Common PDF errors: Forgetting to show work, omitting units, skipping verification steps, poor diagram quality.
PDF success strategies: Neat handwriting, clear formulas, labeled diagrams, organized steps.
Essential PDF formulas:

• Rectangle: \(P = 2 \times (length + width)\)

• Square: \(P = 4 \times side\)

• Triangle: \(P = side_1 + side_2 + side_3\)

• Equilateral Triangle: \(P = 3 \times side\)

• Missing Length: \(length = (perimeter \div 2) - width\)

• PDF Format: Always show formulas and calculations

PDF Worksheet Solutions: Exercises 4 to 5
4 Composite shape perimeter
Exercise 4
A shape is made by placing a square with sides of 6 cm on top of a rectangle with dimensions 8 cm by 6 cm. What is the perimeter of the combined shape? Include a labeled diagram in your PDF worksheet.
Definition:

Composite Shape Perimeter: Only count the outer edges, not internal connections. Essential for PDF worksheet accuracy.

Dimensions
Square: 6×6cm, Rectangle: 8×6cm
External sides
8+6+8+6+6+6
Result
P = 40cm
Step 1: Visualize the composite shape

Square (6×6cm) sits on top of rectangle (8×6cm), sharing one 6cm side

Step 2: Identify all external sides for PDF

Bottom rectangle: bottom (8cm), left (6cm), right (6cm)

Square: left (6cm), right (6cm), top (6cm)

Shared side (6cm) is internal, not part of perimeter

Step 3: Add all external sides

Perimeter = 8 + 6 + 6 + 6 + 6 + 6 = 40 cm

Step 4: Create labeled diagram for PDF

Draw composite shape with all external dimensions marked

Step 5: Verify and present solution

Double-check counting of external sides before submitting PDF

The perimeter of the combined shape is 40 cm
Final answer:

The perimeter of the combined shape is 40 centimeters. Diagram shows composite shape with external sides labeled.

Applied rules:

• Composite Perimeter: Only count outer edges

• Shared Sides: Internal connections don't contribute to perimeter

• PDF Quality: Include clear, labeled diagrams

5 Real-world PDF application
Exercise 5
A school wants to install a fence around a rectangular playground that is 50 meters long and 30 meters wide. If fencing costs $4 per meter, how much will it cost to fence the entire playground? Show all calculations in your PDF worksheet.
Definition:

Cost Application: First find the perimeter, then multiply by the cost per unit length. Perfect for PDF worksheet multi-step problems.

Given
Length = 50m, Width = 30m, Cost = $4/m
Steps
P = 2(l+w), Cost = P × rate
Result
$640
Step 1: Find the perimeter of the playground

Perimeter = 2 × (length + width)

Perimeter = 2 × (50 + 30) = 2 × 80 = 160 meters

Step 2: Calculate the total cost

Cost = Perimeter × Cost per meter

Cost = 160 × $4 = $640

Step 3: Show all work for PDF

Formula: P = 2(l + w) = 2(50 + 30) = 160m

Cost calculation: 160m × $4/m = $640

Step 4: Verify calculations

Perimeter check: 2 × (50 + 30) = 2 × 80 = 160 ✓

Cost check: 160 × 4 = 640 ✓

Step 5: Present final answer

The total cost to fence the playground is $640

The total cost to fence the playground is $640
Final answer:

The school will need $640 to fence the entire rectangular playground. All calculations shown above.

Applied rules:

• Rectangle Perimeter: P = 2(length + width)

• Cost Calculation: Total Cost = Perimeter × Rate per unit

• PDF Format: Show all steps clearly with formulas

Complete PDF Worksheet Guide for Grade 4
Rectangle: \(P = 2(l + w)\)
PDF Perimeter Concepts
Key definitions:

Perimeter: The distance around the outside of a shape

Rectangle: A 4-sided shape with 4 right angles and opposite sides equal

Square: A rectangle with all 4 sides equal

Equilateral Triangle: A triangle with all 3 sides equal

Composite Shape: A shape made by combining two or more basic shapes

PDF Worksheet: Structured practice materials designed for organized learning and assessment

PDF Worksheet methodology:
  1. Read thoroughly: Understand the problem requirements
  2. Identify shapes: Determine which geometric shapes are involved
  3. Select formulas: Use the appropriate perimeter formula
  4. Show all work: Write formulas and calculations clearly
  5. Create diagrams: Draw shapes when requested
  6. Verify answers: Check calculations before submission
  7. Include units: Always add proper measurement units
Tip 1: For PDF worksheets, always write the formula before substituting values.
Tip 2: Draw diagrams neatly with a ruler for better presentation in PDF format.
Tip 3: Box or highlight your final answers in PDF worksheets.
Tip 4: Always verify your answers by substituting back into the original formula for PDF submissions.
Common PDF errors: Skipping steps, forgetting to show formulas, omitting units, poor diagram quality.
PDF success strategies: Organized work, clear labeling, neat diagrams, systematic approach.
Essential PDF formulas for grade 4:

• Rectangle: \(P = 2 \times (length + width)\)

• Square: \(P = 4 \times side\)

• Triangle: \(P = side_1 + side_2 + side_3\)

• Equilateral Triangle: \(P = 3 \times side\)

• Missing Length: \(length = (perimeter \div 2) - width\)

• Cost Problems: \(total\_cost = perimeter \times cost\_per\_unit\)

• PDF Rule: Always show your work and formulas clearly

PDF Worksheet Features & Benefits
PDF Learning Tools
PDF worksheet advantages:
Structured format for organized learning
Printable for offline practice
Shareable for classroom use

Benefits: PDF worksheets provide structured practice for perimeter problems.

  • Structured format ensures systematic learning
  • Printable for hands-on practice
  • Shareable across classrooms and homes
  • Standardized format for assessment

Questions & Answers

Question: How should I format perimeter problems in PDF worksheets for grade 4 students?

Answer: Here's the recommended format for perimeter PDF worksheets:

  • Clear problem statement: Begin with a well-worded word problem
  • Space for work: Provide adequate space for students to show their calculations
  • Formula boxes: Include spaces for students to write the appropriate formulas
  • Diagram areas: Leave space for students to draw shapes when needed
  • Unit prompts: Remind students to include units in their answers

Example format: Problem → Formula → Work Space → Diagram Space → Answer Box. This structured approach helps students organize their thinking and makes grading easier.

Question: My child struggles with PDF worksheets because they don't know how to show their work properly. Any advice?

Answer: Here's a systematic approach to help your child with PDF worksheets:

  1. Read first: Have them read the problem twice before starting
  2. Circle key info: Identify what's given and what's needed
  3. Write the formula: Always write the perimeter formula first
  4. Show substitution: Write the formula with values substituted
  5. Calculate step by step: Show each mathematical step
  6. Include units: Always write the correct units in the final answer

Practice this format consistently with several problems until it becomes natural. This systematic approach works well for PDF submissions.

Question: What if I don't know how to draw the shape for a PDF worksheet problem?

Answer: Don't worry about perfect drawings! For PDF worksheets, simple diagrams work well:

  • Use a ruler: Draw straight lines for rectangles and squares
  • Label clearly: Write the measurements next to each side
  • Keep it simple: A rough but accurate sketch is fine
  • Focus on accuracy: Make sure the proportions are somewhat correct

Example: For a rectangle with length 8 and width 5, draw a rectangle, label one long side as 8 and one short side as 5. The diagram helps you visualize which sides to add for the perimeter.

Remember: The diagram is for YOUR understanding, so it doesn't need to be perfect!