Solved Exercises on Understanding Perimeter in Grade 3

Master understanding perimeter: finding perimeter of shapes, comparing perimeters, and solving perimeter word problems through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Perimeter of rectangle
Exercise 1
Find the perimeter of a rectangle that is 5 units long and 3 units wide.
Definition:

Perimeter: The distance around the outside of a shape, found by adding all side lengths

Perimeter calculation method:
  1. Identify all side lengths of the shape
  2. Add all the side lengths together
  3. For rectangles: Add length + width + length + width
  4. Express the answer in linear units
Length
5 units
Width
3 units
Perimeter
5+3+5+3=16
Step 1: Identify the side lengths

A rectangle has 2 lengths and 2 widths

Step 2: List all side lengths

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

Step 3: Add all sides

Perimeter = 5 + 3 + 5 + 3 = 16 units

5 units
3 units
5 units
3 units
Perimeter = 16 units
Final answer:

The perimeter of the rectangle is 16 units

Applied rules:

• Perimeter definition: Distance around the shape

• Addition: Sum all side lengths

• Rectangle property: Opposite sides are equal

2 Perimeter of square
Exercise 2
What is the perimeter of a square with sides of 4 units?
Definition:

Square perimeter: The distance around a square, calculated by adding all four equal sides

Side Length
4 units
Number of Sides
4 sides
Perimeter
4 × 4 = 16
Step 1: Identify the side length

All sides = 4 units (square property)

Step 2: Count the sides

A square has 4 equal sides

Step 3: Add all sides

Perimeter = 4 + 4 + 4 + 4 = 16 units

Step 4: Verify with multiplication

Alternatively: 4 × 4 = 16 units

4 units
4 units
4 units
4 units
Perimeter = 16 units
Final answer:

The perimeter of the square is 16 units

Applied rules:

• Square property: All sides are equal

• Perimeter formula: Perimeter = 4 × Side

• Multiplication: Faster than repeated addition

3 Perimeter of triangle
Exercise 3
A triangle has sides measuring 3 units, 4 units, and 5 units. What is its perimeter?
Definition:

Triangle perimeter: The distance around a triangle, found by adding all three side lengths

Side 1
3 units
Side 2
4 units
Side 3
5 units
Perimeter
3+4+5=12
Step 1: Identify all three sides

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

Step 2: Add all sides together

Perimeter = 3 + 4 + 5 = 12 units

Step 3: Express the final answer

Perimeter = 12 units

Step 4: Verify the calculation

Check: 3 + 4 + 5 = 12 ✓

5 units
4 units
3 units
Perimeter = 12 units
Final answer:

The perimeter of the triangle is 12 units

Applied rules:

• Triangle perimeter: Sum of all three sides

• Addition: Add all side lengths

• Verification: Check calculation for accuracy

Perimeter Fundamentals
\text{Perimeter} = \text{Sum of All Side Lengths}
Perimeter Formula
Rectangle
2(L+W)
Two lengths + two widths
Square
4S
Four equal sides
Triangle
S1+S2+S3
Three sides added
Key definitions:

Perimeter: The distance around the outside of a shape

Side length: The measurement of one edge of a shape

Linear unit: The unit used to measure distance (inches, feet, centimeters, etc.)

Regular polygon: A shape with all sides equal

3-step perimeter method:
  1. Identify: Find all side lengths of the shape
  2. Add: Sum all the side lengths together
  3. Express: State the answer in linear units
Tip 1: Always include all sides in your calculation.
Tip 2: For rectangles: multiply length by 2, multiply width by 2, then add.
Tip 3: For squares: multiply side length by 4.
Tip 4: Always include the unit in your answer (units, feet, cm, etc.).
Common errors: Forgetting to add all sides, not including units, miscounting side lengths.
Memory aid: "Perimeter is the fence around the yard - add all sides!"
Key perimeter facts:

• Perimeter measures the outside distance of a shape

• Perimeter is always measured in linear units

• Rectangle perimeter = 2(length + width)

• Square perimeter = 4 × side length

Solution: Exercises 4 to 5
4 Irregular shape perimeter
Exercise 4
Find the perimeter of an L-shaped figure with sides measuring 2, 3, 2, 1, 4, and 2 units.
Definition:

Irregular shape perimeter: Finding the perimeter of shapes with unequal sides by adding all side lengths

Side Lengths
2+3+2+1+4+2
Addition
14 units
Step 1: List all side lengths

Sides: 2, 3, 2, 1, 4, 2 units

Step 2: Add all sides together

Perimeter = 2 + 3 + 2 + 1 + 4 + 2 = 14 units

Step 3: Verify the calculation

Check: 2 + 3 = 5, 5 + 2 = 7, 7 + 1 = 8, 8 + 4 = 12, 12 + 2 = 14 ✓

Perimeter = 14 units
Final answer:

The perimeter of the L-shaped figure is 14 units

Applied rules:

• Irregular shapes: Add all side lengths regardless of equality

• Systematic addition: Add in order to avoid missing any

• Verification: Check calculation step by step

5 Perimeter comparison
Exercise 5
A square has sides of 5 units. A rectangle has sides of 4 units and 6 units. Which shape has the larger perimeter?
Definition:

Perimeter comparison: Calculating and comparing perimeters of different shapes

Square Perimeter
4 × 5 = 20
Rectangle Perimeter
2(4+6)=20
Comparison
20 = 20
Step 1: Calculate square perimeter

Perimeter = 4 × 5 = 20 units

Step 2: Calculate rectangle perimeter

Perimeter = 2(4 + 6) = 2(10) = 20 units

Step 3: Compare the perimeters

20 = 20, so both perimeters are equal

Step 4: State the conclusion

Both shapes have the same perimeter

5 units
5 units
5 units
5 units
6 units
4 units
6 units
4 units
Square: 20 units | Rectangle: 20 units
Final answer:

Both shapes have the same perimeter (20 units each)

Applied rules:

• Square perimeter: 4 × side length

• Rectangle perimeter: 2 × (length + width)

• Comparison: Compare calculated perimeters

Complete Perimeter Understanding Guide
\text{Perimeter} = \sum \text{Side Lengths}
Universal Perimeter Formula
Key definitions:

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

Linear measurement: Measurement in straight-line units (inches, feet, centimeters, etc.)

Regular polygon: A shape with all sides and angles equal

Irregular polygon: A shape with sides and/or angles of different measures

Advanced perimeter techniques:
  1. Visual tracking: Trace the perimeter with your finger to ensure all sides are counted
  2. Organized calculation: Write down each side length before adding
  3. Formula application: Use specific formulas for regular shapes
  4. Verification: Double-check by recounting or using an alternate method
Tip 1: Practice with real objects like picture frames or books.
Tip 2: Draw the shape and label each side before calculating.
Tip 3: Use the phrase "fence around the yard" to remember perimeter means outside distance.
Tip 4: For complex shapes, break them into simpler parts to find the perimeter.
Common errors: Forgetting to add all sides, confusing perimeter with area, not including units.
Success strategies: Regular practice, visual aids, real-world connections.
Essential perimeter facts:

• Perimeter measures the boundary of a shape

• Perimeter is always expressed in linear units

• Rectangle: P = 2(L + W)

• Square: P = 4S

• Triangle: P = S1 + S2 + S3

Perimeter Shape Comparison
Perimeter vs Shape Type
Understanding how different shapes with the same area can have different perimeters:
Square vs Rectangle vs Triangle

Shape Perimeters:

  • Square (3×3): Perimeter = 4 × 3 = 12 units
  • Rectangle (2×4): Perimeter = 2(2+4) = 12 units
  • Rectangle (1×5): Perimeter = 2(1+5) = 12 units
  • Triangle (3-4-5): Perimeter = 3+4+5 = 12 units

Questions & Answers

Question: How is perimeter different from area? I sometimes get them confused.

Answer: Here's how to remember the difference:

  • Perimeter: The distance around the outside of a shape (like a fence around a yard)
  • Area: The space inside a shape (like the grass inside the yard)
  • Units: Perimeter uses linear units (feet, inches), Area uses square units (square feet, square inches)

Think of it this way: If you walk around the edge of a garden, you're measuring perimeter. If you cover the ground inside the garden with soil, you're measuring area.

Perimeter = "around", Area = "inside"!

Question: Do I always have to add all the sides? Can't I just multiply for rectangles?

Answer: You can use multiplication for rectangles because opposite sides are equal:

  • Method 1 (Addition): Add all 4 sides: L + W + L + W
  • Method 2 (Multiplication): Use the formula: 2(L + W)
  • Both give the same result: For a 4×6 rectangle: 4+6+4+6 = 20 or 2(4+6) = 20

For other shapes like triangles or irregular polygons, you must add all sides individually.

The multiplication shortcut only works for shapes with equal opposite sides!

Question: What if a shape has sides with decimals or fractions? How do I find the perimeter?

Answer: The process is exactly the same! You still add all the side lengths:

  • Example: A triangle with sides 2.5, 3.7, and 4.8 units
  • Perimeter: 2.5 + 3.7 + 4.8 = 11.0 units
  • Rule: Perimeter = sum of all side lengths, regardless of the numbers

For now in grade 3, focus on whole numbers. Decimal and fraction calculations come in later grades.

The important thing is to understand that perimeter always means adding all the sides!

. .