Basic Perimeter Word Problems for Grade 3

Master basic perimeter calculations: rectangles, squares, and triangles through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Rectangle perimeter
Exercise 1
A rectangular garden has a length of 8 meters and a width of 5 meters. What is the perimeter of the garden?
Definition:

Perimeter: The distance around the outside of a shape. For a rectangle: \(P = 2 \times (length + width)\)

Perimeter calculation method:
  1. Find the length and width of the rectangle
  2. Add the length and width together
  3. Multiply the sum by 2
  4. Write the answer with the unit (meters)
Given
Length = 8m, Width = 5m
Formula
P = 2(l + w)
Result
P = 26m
Step 1: Identify the measurements

Length = 8 meters, Width = 5 meters

Step 2: Write down the formula

Perimeter = 2 × (length + width)

Step 3: Add length and width

8 + 5 = 13

Step 4: Multiply by 2

2 × 13 = 26

Step 5: Write the answer with units

The perimeter is 26 meters

The perimeter of the garden is 26 meters
Final answer:

The perimeter of the rectangular garden is 26 meters

Applied rules:

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

• Add first: Calculate inside parentheses first

• Always include units: Write meters after the number

2 Square perimeter
Exercise 2
A square picture frame has sides of 6 inches each. What is the perimeter of the frame?
Definition:

Square Perimeter: Since all sides are equal, \(P = 4 \times side\)

Given
Side = 6 in
Formula
P = 4s
Result
P = 24 in
Step 1: Identify the side length

All sides of a square are equal: Side = 6 inches

Step 2: Write down the formula

Perimeter = 4 × side length

Step 3: Multiply by 4

4 × 6 = 24

Step 4: Write the answer with units

The perimeter is 24 inches

The perimeter of the frame is 24 inches
Final answer:

The perimeter of the square picture frame is 24 inches

Applied rules:

• Square Perimeter: P = 4 × side length

• All sides equal: In a square, all four sides are the same length

• Always include units: Write inches after the number

3 Triangle perimeter
Exercise 3
A triangular sandbox has sides measuring 4 feet, 5 feet, and 3 feet. What is the perimeter of the sandbox?
Definition:

Triangle Perimeter: Sum of all three sides, \(P = a + b + c\)

Given
Sides: 4ft, 5ft, 3ft
Formula
P = a + b + c
Result
P = 12ft
Step 1: Identify all three sides

Side 1 = 4 feet, Side 2 = 5 feet, Side 3 = 3 feet

Step 2: Write down the formula

Perimeter = Side 1 + Side 2 + Side 3

Step 3: Add all sides together

4 + 5 + 3 = 12

Step 4: Write the answer with units

The perimeter is 12 feet

The perimeter of the sandbox is 12 feet
Final answer:

The perimeter of the triangular sandbox is 12 feet

Applied rules:

• Triangle Perimeter: P = sum of all three sides

• Addition: Add all measurements together

• Always include units: Write feet after the number

Basic Perimeter Rules and Methods
Rectangle: \(P = 2(l + w)\)
Rectangle Perimeter
Square
\(P = 4s\)
Perimeter of Square
Triangle
\(P = a + b + c\)
Perimeter of Triangle
Any Shape
\(P = \text{sum of all sides}\)
General Rule
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

Triangle: A 3-sided shape

Basic methodology:
  1. Read the problem: Find out what shape it is
  2. Find the measurements: Look for the lengths of the sides
  3. Choose the right formula: Use rectangle, square, or triangle formula
  4. Calculate: Do the math carefully
  5. Write the answer: Don't forget the units!
Tip 1: Perimeter means "around the outside" - imagine walking around the shape.
Tip 2: Draw a picture to help you see the shape and its sides.
Tip 3: Always write down the formula before you solve.
Tip 4: Check if your answer makes sense compared to the given numbers.
Common errors: Forgetting to multiply by 2 for rectangles, adding instead of multiplying for squares, forgetting units.
Key memorization: Rectangle P=2(l+w), Square P=4s, Triangle P=a+b+c.
Formulas to remember:

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

• Square Perimeter: \(P = 4 \times side\)

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

• Any Shape: \(P = \text{add all sides}\)

Solution: Exercises 4 to 5
4 Mixed shapes
Exercise 4
A rectangular tablecloth is 4 feet long and 3 feet wide. What is the perimeter of the tablecloth? If a square napkin has sides of 8 inches, what is its perimeter?
Definition:

Mixed Problems: Problems with different shapes requiring different formulas.

Tablecloth
P = 2(4 + 3)
Napkin
P = 4 × 8
Results
14ft, 32in
Step 1: Solve for the rectangle

Length = 4 feet, Width = 3 feet

Perimeter = 2 × (4 + 3) = 2 × 7 = 14 feet

Step 2: Solve for the square

Side = 8 inches

Perimeter = 4 × 8 = 32 inches

Step 3: Write both answers

Tablecloth perimeter: 14 feet

Napkin perimeter: 32 inches

Step 4: Check units

Each answer has the correct units for its shape

Tablecloth: 14 feet, Napkin: 32 inches
Final answer:

The perimeter of the tablecloth is 14 feet, and the perimeter of the napkin is 32 inches.

Applied rules:

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

• Square Formula: P = 4 × side

• Multiple Shapes: Solve each shape separately

5 Real-world application
Exercise 5
Tom wants to put a fence around his rectangular vegetable garden. The garden is 10 feet long and 7 feet wide. How many feet of fencing does he need?
Definition:

Real-world Perimeter: The amount of material needed to go around a shape.

Given
Length = 10ft, Width = 7ft
Formula
P = 2(l + w)
Result
P = 34ft
Step 1: Identify what you need to find

Tom needs fencing for the garden, which means finding the perimeter

Step 2: Identify the shape and measurements

Rectangular garden: Length = 10 feet, Width = 7 feet

Step 3: Write down the rectangle formula

Perimeter = 2 × (length + width)

Step 4: Add length and width

10 + 7 = 17

Step 5: Multiply by 2

2 × 17 = 34

Step 6: State the answer with units

Tom needs 34 feet of fencing

Tom needs 34 feet of fencing
Final answer:

Tom needs 34 feet of fencing to surround his garden

Applied rules:

• Real-world Context: Perimeter = amount of material needed

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

• Units: Answer must match the unit of measurement given

Complete Perimeter Summary for Grade 3
Rectangle: \(P = 2(l + w)\)
Basic 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

Triangle: A 3-sided shape

Basic methodology:
  1. Look at the shape: Is it a rectangle, square, or triangle?
  2. Find the measurements: What are the lengths of the sides?
  3. Pick the right formula: Use the correct perimeter formula
  4. Do the math: Calculate carefully
  5. Write the answer: Include the units (feet, inches, meters)
Tip 1: Draw the shape and write the measurements on it to help visualize.
Tip 2: For rectangles, add the length and width first, then multiply by 2.
Tip 3: For squares, just multiply one side by 4 since all sides are equal.
Tip 4: Always double-check that you added all sides correctly.
Common errors: Forgetting to multiply by 2 in rectangle formula, counting sides twice, forgetting units.
Memory tricks: Rectangle: "double the sum of length and width"; Square: "4 times any side"; Triangle: "add all three sides".
Essential formulas:

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

• Square: \(P = 4 \times side\)

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

• Any shape: \(P = \text{add all sides}\)

• Always include units: feet, inches, meters, etc.

Basic Perimeter Examples
Perimeter Calculations
Simple perimeter examples:
Square: side = 5 units → P = 20 units
Rectangle: l=6, w=4 → P = 20 units
Triangle: sides 3,4,5 → P = 12 units

Examples: These show how to calculate perimeter for basic shapes.

  • Square: 4 × side = 4 × 5 = 20 units
  • Rectangle: 2 × (6 + 4) = 2 × 10 = 20 units
  • Triangle: 3 + 4 + 5 = 12 units

Questions & Answers

Question: Why do we multiply by 2 for rectangles but by 4 for squares? They both have 4 sides!

Answer: Great observation! The reason is that rectangles and squares have different side properties:

  • A rectangle has 2 pairs of equal sides: 2 long sides and 2 short sides. So the perimeter is: long + short + long + short = 2×long + 2×short = 2×(long + short)
  • A square has 4 equal sides. So the perimeter is: side + side + side + side = 4×side

Actually, if you use the rectangle formula for a square (where length = width = side), you get: P = 2×(side + side) = 2×(2×side) = 4×side. Both formulas work, but the square formula is simpler!

Example: For a square with sides of 5cm: Rectangle formula gives P = 2×(5+5) = 2×10 = 20cm, and square formula gives P = 4×5 = 20cm. Same result!

Question: My child often forgets to include units in their answers. How important is this?

Answer: Including units is extremely important for several reasons:

  • Makes the answer meaningful: Numbers without units don't tell the whole story. 10 could mean 10 inches, 10 feet, or 10 miles!
  • Shows understanding: Using units demonstrates that your child understands what they're measuring
  • Prevents mistakes: Units help catch errors in calculations
  • Real-world application: In everyday life, we always use units when measuring

Example: If the perimeter is 24, that's incomplete. But 24 feet tells us exactly how far around the shape goes. Always encourage your child to write the unit after their answer!

Question: How can I remember which formula to use for each shape?

Answer: Here are some memory tricks to help remember the formulas:

  • Rectangle: "Double the sum of length and width" → P = 2×(l + w)
  • Square: "Four times any side" → P = 4×s
  • Triangle: "Add all three sides" → P = a + b + c

You can also remember that:

  • Rectangles have opposite sides equal (2 long, 2 short)
  • Squares have all 4 sides the same
  • Triangles always have 3 sides to add

Practice drawing each shape and writing the formula next to it. The more you practice, the easier it will be to remember!