Perimeter and Area Practice Worksheets for 4th Grade

Complete practice worksheets on perimeter and area calculations: rectangles, squares, and composite shapes with visual diagrams and step-by-step solutions.

Practice Worksheet Problems
1 Basic Perimeter
Problem 1
A rectangular room measures 10 feet long and 7 feet wide. What is the perimeter of the room? Draw a picture and label the sides.
10 ft
7 ft
P = ?
Step 1: Identify dimensions

Length = 10 feet, Width = 7 feet

Step 2: Apply perimeter formula

P = 2 × (length + width)

P = 2 × (10 + 7)

Step 3: Calculate

P = 2 × 17 = 34 feet

Perimeter = 34 feet
2 Area Calculation
Problem 2
A square garden has sides that are 9 meters long. What is the area of the garden? If each square meter can grow 4 plants, how many plants can fit in the entire garden?
9 m
9 m
A = ?
Step 1: Find the area of the square

Area = side × side = 9 × 9 = 81 square meters

Step 2: Calculate number of plants

Plants per square meter = 4

Total plants = 81 × 4 = 324 plants

Area = 81 m², Plants = 324
3 Multiplicative Comparison
Problem 3
Rectangle A has a length of 8 cm and a width of 5 cm. Rectangle B has the same width but its length is 3 times longer than Rectangle A. Compare the perimeters and areas of both rectangles.
8 cm
5 cm
A₁ = ?
24 cm
5 cm
A₂ = ?
Step 1: Find dimensions of Rectangle A

Length = 8 cm, Width = 5 cm

Perimeter = 2×(8+5) = 26 cm

Area = 8×5 = 40 cm²

Step 2: Find dimensions of Rectangle B

Length = 3×8 = 24 cm, Width = 5 cm

Perimeter = 2×(24+5) = 58 cm

Area = 24×5 = 120 cm²

Step 3: Compare results

Perimeter ratio: 58÷26 ≈ 2.23 (about 2.23 times larger)

Area ratio: 120÷40 = 3 (exactly 3 times larger)

Rectangle B: P=58cm, A=120cm²
Detailed Solutions and Explanations
Solution 1: Perimeter Calculation
Concept:

Perimeter: The total distance around the outside of a shape. For rectangles, P = 2×(length + width)

Steps:
  1. Identify length and width: 10 ft and 7 ft
  2. Add the length and width: 10 + 7 = 17
  3. Multiply by 2: 2 × 17 = 34 ft
Key Rule:

Perimeter is always measured in linear units (ft, cm, m)

Answer:

The perimeter of the room is 34 feet.

Solution 2: Area and Multiplication
Concept:

Area: The amount of space inside a 2D shape. For squares, A = side × side

Steps:
  1. Calculate area: 9 × 9 = 81 square meters
  2. Multiply by plants per square meter: 81 × 4 = 324 plants
Key Rule:

Area is always measured in square units (ft², cm², m²)

Answer:

The area is 81 square meters, and 324 plants can fit in the garden.

Solution 3: Multiplicative Comparison
Concept:

Multiplicative comparison: Comparing quantities using multiplication (times larger)

Steps:
  1. Calculate Rectangle A: P = 26 cm, A = 40 cm²
  2. Calculate Rectangle B: Length = 3×8=24 cm, P = 58 cm, A = 120 cm²
  3. Compare: P ratio ≈ 2.23, A ratio = 3
Key Rule:

When one dimension is multiplied by n, area changes by factor n, but perimeter changes differently

Answer:

Rectangle B has a perimeter about 2.23 times larger and an area exactly 3 times larger than Rectangle A.

Comprehensive Summary and Study Guide
Key Concepts and Definitions
Perimeter

Definition: The total distance around the outside of a shape.

Formula (Rectangle): P = 2 × (length + width)

Formula (Square): P = 4 × side

Units: Linear measurements (cm, m, ft, in)

Area

Definition: The amount of space inside a 2D shape.

Formula (Rectangle): A = length × width

Formula (Square): A = side × side

Units: Square measurements (cm², m², ft², in²)

Multiplicative Comparison

Definition: Comparing quantities using multiplication.

Example: "3 times larger" means multiply by 3.

Method: Divide larger quantity by smaller to find ratio.

Step-by-Step Methods
Solving Perimeter Problems:
  1. Identify the shape: Rectangle, square, or composite figure
  2. Find all dimensions: Measure or identify given lengths
  3. Select the formula: P = 2(l+w) for rectangles, P = 4s for squares
  4. Substitute values: Replace variables with known numbers
  5. Calculate: Perform the arithmetic operations
  6. Label: Include correct linear units
Solving Area Problems:
  1. Identify the shape: Rectangle, square, or composite figure
  2. Find dimensions: Length and width (or base and height)
  3. Select the formula: A = l×w for rectangles, A = s² for squares
  4. Substitute values: Replace variables with known numbers
  5. Calculate: Perform the multiplication
  6. Label: Include correct square units
Solving Multiplicative Comparison:
  1. Identify the quantities: Find the two values being compared
  2. Determine the relationship: Which is larger? By what factor?
  3. Set up the equation: Larger = Factor × Smaller
  4. Solve for the unknown: Use division or multiplication as needed
  5. Verify: Check that your answer makes sense
Tips and Tricks
Tip 1: Always draw a diagram and label dimensions to visualize the problem.
Tip 2: Remember: perimeter is linear (cm, m) and area is square (cm², m²).
Tip 3: For multiplicative comparisons, divide the larger number by the smaller to find the factor.
Tip 4: Check your work by ensuring units match the concept (linear vs. square).
Tip 5: For composite figures, break them into simpler shapes first.
Common Mistakes to Avoid
Mistake 1: Confusing perimeter and area formulas. Remember: P = 2(l+w), A = l×w
Mistake 2: Forgetting to include units in your final answer.
Mistake 3: Using wrong units (linear instead of square or vice versa).
Mistake 4: Misreading multiplicative comparison problems ("times larger" vs "more than").

Questions & Answers

Question: Why do we multiply by 2 when finding the perimeter of a rectangle? Why not just add the length and width once?

Answer: Great question! When finding the perimeter of a rectangle, we need to count ALL the sides. A rectangle has 4 sides:

  • One length (top side)
  • One width (right side)
  • One length (bottom side)
  • One width (left side)

So the perimeter is: length + width + length + width = 2×length + 2×width = 2×(length + width)

Think of walking around the rectangle - you walk the length twice and the width twice, so you need to count each dimension twice.

Question: My child struggles with word problems involving perimeter and area. How can I help them understand what operation to use?

Answer: Word problems can be tricky! Here's a strategy to help your child:

  • Look for key words: "around," "fence," "border," "edge" usually mean perimeter; "cover," "space," "inside," "surface" usually mean area
  • Draw a picture: Have them sketch the situation described
  • Label dimensions: Write the given measurements on their drawing
  • Ask: "Am I measuring the outside or the inside?"

Practice with real-world examples: "If we want to put a fence around the yard, are we measuring the fence (perimeter) or the grass (area)?"

Start with simple problems and gradually increase complexity as they gain confidence.

Question: How can I help my students understand the relationship between changing dimensions and the effect on perimeter and area?

Answer: This is a fundamental concept! Use hands-on activities:

  • Grid paper: Have students draw rectangles and count squares to see area change
  • String or yarn: Use to trace perimeters of different shapes
  • Manipulatives: Pattern blocks or tiles to build shapes

Key relationships to emphasize:

  • If you double one dimension, area doubles but perimeter increases by less than double
  • If you double both dimensions, area quadruples (2×2=4) but perimeter doubles
  • Shapes with the same perimeter can have different areas

Create tables showing dimensions, perimeter, and area side by side so students can see the patterns emerge.