Solved Exercises on Perimeter Word Problems in Grade 3

Master perimeter calculations: rectangles, squares, irregular shapes, and real-world applications through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Rectangle Perimeter
Exercise 1
Sarah wants to put a fence around her rectangular garden. The garden is 8 feet long and 5 feet wide. How many feet of fencing does she need?
Definition:

Perimeter: The total distance around the outside of a shape

Rectangle: A 4-sided shape with opposite sides equal and all angles 90°

Rectangle Perimeter Method:
  1. Identify length and width
  2. Apply the formula: Perimeter = 2 × (length + width)
  3. Add up all four sides
Length = 8 ft
Length = 8 ft
Width = 5 ft
Width = 5 ft
Given
Length = 8 ft, Width = 5 ft
Formula
P = 2(l + w)
Result
26 ft
Step 1: Identify the given information

Length = 8 feet, Width = 5 feet

Step 2: Apply the rectangle perimeter formula

Perimeter = 2 × (length + width)

Perimeter = 2 × (8 + 5)

Step 3: Calculate the sum inside parentheses

8 + 5 = 13

Step 4: Multiply by 2

2 × 13 = 26

Sarah needs 26 feet of fencing
Final answer:

Sarah needs 26 feet of fencing for her garden.

Applied rules:

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

• Order of Operations: Solve parentheses first, then multiply

• Units: Always include the unit of measurement

2 Square Perimeter
Exercise 2
Tom is making a square picture frame. Each side of the frame is 12 inches long. How much wood does he need for the frame?
Definition:

Square: A 4-sided shape with all sides equal and all angles 90°

Perimeter: The total distance around the outside of a shape

Side = 12 in
Side = 12 in
Side = 12 in
Side = 12 in
Given
Side = 12 in
Formula
P = 4 × side
Result
48 in
Step 1: Identify the given information

All sides of the square are 12 inches long

Step 2: Apply the square perimeter formula

Perimeter = 4 × side length

Perimeter = 4 × 12

Step 3: Calculate the multiplication

4 × 12 = 48

Tom needs 48 inches of wood
Final answer:

Tom needs 48 inches of wood for his square picture frame.

Applied rules:

• Square Perimeter: P = 4 × side length

• Equal Sides: All 4 sides of a square are equal

• Units: Always include the unit of measurement

3 Irregular Shape Perimeter
Exercise 3
A playground has the shape of an L. The sides measure 6 m, 4 m, 2 m, 3 m, 4 m, and 1 m. What is the perimeter of the playground?
Definition:

Irregular Shape: A shape with sides of different lengths

Perimeter: The total distance around the outside of any shape

6m
4m
4m
1m
Given
Sides: 6, 4, 2, 3, 4, 1 m
Method
Add all sides
Result
20 m
Step 1: List all the side lengths

6 m, 4 m, 2 m, 3 m, 4 m, 1 m

Step 2: Add all the sides together

Perimeter = 6 + 4 + 2 + 3 + 4 + 1

Step 3: Calculate the sum

6 + 4 = 10, 10 + 2 = 12, 12 + 3 = 15, 15 + 4 = 19, 19 + 1 = 20

The perimeter is 20 meters
Final answer:

The perimeter of the playground is 20 meters.

Applied rules:

• Irregular Perimeter: Add all side lengths

• Order Addition: Group numbers to make calculation easier

• Units: Always include the unit of measurement

Perimeter Rules and Methods
Rectangle: P = 2(l + w)
Rectangle Perimeter
Square: P = 4s
Square Perimeter
Definition
Perimeter
Total distance around a shape
Rectangle
P = 2(l + w)
Length + Width × 2
Square
P = 4s
Side × 4
Irregular
P = sum of all sides
Add all sides
Key definitions:

Perimeter: The distance around the outside of a shape

Rectangle: 4-sided shape with opposite sides equal

Square: 4-sided shape with all sides equal

Complete methodology:
  1. Read the problem: Identify the shape and given measurements
  2. Choose the method: Rectangle, square, or irregular shape formula
  3. Apply the formula: Substitute known values
  4. Calculate: Perform the arithmetic
  5. Check units: Include appropriate measurement units
Tip 1: Draw the shape and label the sides to visualize the problem.
Tip 2: Remember that perimeter is always measured in linear units (feet, inches, meters).
Tip 3: For rectangles, you only need length and width - don't count all four sides separately.
Tip 4: For irregular shapes, add ALL the side lengths together.
Common errors: Forgetting to multiply by 2 in rectangles, counting each side individually instead of using formulas.
Exam preparation: Memorize formulas, practice word problems, pay attention to units.
Formulas to know by heart:

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

• Square Perimeter: P = 4 × side length

• Irregular Shape Perimeter: Add all side lengths

• Always include units in your final answer

Solution: Exercises 4 to 5
4 Real-World Application
Exercise 4
Emma wants to put ribbon around a rectangular gift box that is 10 inches long and 6 inches wide. She has 30 inches of ribbon. Does she have enough ribbon? If not, how much more does she need?
Definition:

Real-World Application: Using math to solve practical problems

Comparison: Determining if one amount is greater than, less than, or equal to another

Length = 10 in
Length = 10 in
Width = 6 in
Width = 6 in
Given
Length = 10 in, Width = 6 in, Ribbon = 30 in
Formula
P = 2(l + w)
Result
32 in needed
Step 1: Find the perimeter of the box

Length = 10 inches, Width = 6 inches

Perimeter = 2 × (10 + 6) = 2 × 16 = 32 inches

Step 2: Compare with available ribbon

Ribbon needed: 32 inches

Ribbon available: 30 inches

Step 3: Determine if enough ribbon

32 > 30, so Emma does NOT have enough ribbon

Step 4: Calculate additional ribbon needed

Additional ribbon needed = 32 - 30 = 2 inches

Emma needs 2 more inches of ribbon
Final answer:

No, Emma does not have enough ribbon. She needs 2 more inches of ribbon.

Applied rules:

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

• Comparison: Compare needed vs available amounts

• Subtraction: Find the difference when needed

5 Missing Side Problem
Exercise 5
The perimeter of a rectangle is 24 cm. Its length is 8 cm. What is its width?
Definition:

Missing Side Problem: Finding an unknown dimension when perimeter and one dimension are known

Algebra: Using mathematical operations to find unknown values

Length = 8 cm
Length = 8 cm
Width = ?
Width = ?
Given
P = 24 cm, l = 8 cm
Formula
P = 2(l + w)
Result
w = 4 cm
Step 1: Write the perimeter formula

Perimeter = 2 × (length + width)

24 = 2 × (8 + width)

Step 2: Divide both sides by 2

24 ÷ 2 = (8 + width)

12 = 8 + width

Step 3: Subtract 8 from both sides

12 - 8 = width

4 = width

Step 4: Verify the answer

Perimeter = 2 × (8 + 4) = 2 × 12 = 24 ✓

The width is 4 centimeters
Final answer:

The width of the rectangle is 4 centimeters.

Applied rules:

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

• Algebra: Work backwards to find unknown values

• Verification: Check your answer by substituting back

Perimeter Laws, Methods, Rules, and Definitions
Rectangle: P = 2(l + w)
Rectangle Perimeter Formula
Key definitions:

Perimeter: The total distance around the outside of a 2-dimensional shape

Rectangle: A quadrilateral with four right angles and opposite sides equal

Square: A rectangle with all sides equal

Unit of Measurement: Standard quantity used to express measurements (inches, feet, meters)

Complete methodology:
  1. Read the problem carefully: Identify what shape you're working with
  2. Identify given information: Note all provided measurements
  3. Choose the correct formula: Rectangle, square, or irregular shape
  4. Substitute values: Put known values into the formula
  5. Calculate: Perform the necessary arithmetic
  6. Check your work: Verify calculations and include units
Tip 1: Always draw a diagram when solving word problems to visualize the situation.
Tip 2: In rectangles, you only need length and width - don't count all four sides separately.
Tip 3: For missing side problems, work backwards using algebraic thinking.
Tip 4: Always include the unit of measurement in your final answer.
Common errors: Forgetting to multiply by 2 in rectangle formulas, mixing up length and width, forgetting units.
Key applications: Fencing, framing, border decorations, walking paths, construction projects.
Essential formulas to memorize:

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

• Square Perimeter: P = 4 × side length or P = 4s

• Irregular Shape Perimeter: Add all side lengths together

• Unit Consistency: All measurements must be in the same unit

Problem-solving strategies:

• Look for keywords: "around", "fence", "border", "frame", "edge", "distance"

• Draw diagrams to visualize the problem

• Check if the answer makes sense in the context of the problem

• Verify by substituting back into the original problem when possible

Questions & Answers

Question: I get confused about when to use 2(l+w) and when to use 4s for perimeter. How do I know which one to use?

Answer: Great question! The key is to identify the shape:

  • Use P = 2(l+w) for rectangles, which have two pairs of equal sides (length and width)
  • Use P = 4s for squares, which have four equal sides

Think of it this way: rectangles have different length and width measurements, so you need to account for both. Squares have all sides the same, so you just multiply one side by 4.

Example: A rectangle that's 5 feet long and 3 feet wide → P = 2(5+3) = 16 feet

Example: A square with sides of 4 feet → P = 4×4 = 16 feet

Question: My child struggles with word problems about perimeter. How can I help them understand what to look for?

Answer: Help your child identify key words and strategies:

  • Look for words like "around", "fence", "border", "edge", "walk around", "go around"
  • Encourage drawing a simple diagram of the problem
  • Have them write down what they know (given measurements)
  • Ask: "What am I trying to find?" (the perimeter)

Practice with real-world examples: measuring the perimeter of their bedroom, garden, or a book cover.

Remind them that perimeter is always measured in linear units (feet, inches, meters).

Question: What if I have an odd-shaped figure with different side lengths? How do I find the perimeter?

Answer: For irregular shapes with different side lengths, you simply add up ALL the side lengths!

For example, if you have a shape with sides measuring 3 cm, 5 cm, 4 cm, and 6 cm:

Perimeter = 3 + 5 + 4 + 6 = 18 cm

No special formula needed - just add all the sides together. Count carefully and double-check your addition!

Think of it as taking a walk around the entire edge of the shape - you're measuring every step you take!