Solved Exercises on Perimeter of Irregular Shapes in Grade 3

Master perimeter of irregular shapes: calculating perimeters, identifying sides, applying formulas through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Basic irregular shape
Exercise 1
Find the perimeter of this L-shaped figure:
Side lengths: 5 cm, 3 cm, 2 cm, 4 cm, 2 cm, 1 cm
Definition:

Perimeter: The total distance around the outside of a shape. For irregular shapes, add up all the side lengths.

Perimeter calculation method:
  1. Identify all the sides of the irregular shape
  2. Measure or note the length of each side
  3. Add all the side lengths together
  4. Write the answer with the correct unit
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5 cm
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3 cm
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2 cm
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4 cm
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2 cm
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1 cm
5 + 3 + 2 + 4 + 2 + 1
=
17 cm
Step 1: List all side lengths

Side 1: 5 cm, Side 2: 3 cm, Side 3: 2 cm, Side 4: 4 cm, Side 5: 2 cm, Side 6: 1 cm

Step 2: Add all side lengths

5 + 3 + 2 + 4 + 2 + 1 = 17

Step 3: Write the final answer

The perimeter is 17 cm

Perimeter = 17 cm
Final answer:

The perimeter of the L-shaped figure is 17 cm

Applied rules:

• Perimeter rule: Add all side lengths of the shape

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

• Count all sides: Don't miss any side when adding

2 Complex polygon
Exercise 2
Calculate the perimeter of this house-shaped figure:
Base: 6 m, Left wall: 4 m, Roof left: 3 m, Roof top: 2 m, Roof right: 3 m, Right wall: 4 m
Definition:

Irregular polygon: A shape with straight sides that are not all the same length. To find the perimeter, add all the side lengths.

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3m
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2m
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3m
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4m
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6m
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4m
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6 + 4 + 3 + 2 + 3 + 4
=
22 m
Step 1: Identify all sides

Base: 6 m, Left wall: 4 m, Left roof: 3 m, Roof top: 2 m, Right roof: 3 m, Right wall: 4 m

Step 2: Add all measurements

6 + 4 + 3 + 2 + 3 + 4 = 22

Step 3: Include the unit

Total perimeter = 22 meters

Perimeter = 22 m
Final answer:

The perimeter of the house-shaped figure is 22 meters

Applied rules:

• Complete circuit: Go around the entire shape counting every side

• Order doesn't matter: Addition is commutative (order doesn't affect sum)

• Double-check count: Make sure you counted all sides

3 Multi-sided shape
Exercise 3
Find the perimeter of this 7-sided shape:
Sides: 3 ft, 2 ft, 4 ft, 1 ft, 3 ft, 2 ft, 5 ft
Definition:

Heptagon: A seven-sided polygon. For any polygon, the perimeter is the sum of all its side lengths.

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3ft
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2ft
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4ft
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1ft
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3ft
⬟
2ft
⬟
5ft
3 + 2 + 4 + 1 + 3 + 2 + 5
=
20 ft
Step 1: Count all sides

This shape has 7 sides: 3, 2, 4, 1, 3, 2, 5 feet

Step 2: Add systematically

3 + 2 = 5, then 5 + 4 = 9, then 9 + 1 = 10, then 10 + 3 = 13, then 13 + 2 = 15, then 15 + 5 = 20

Step 3: State the answer

The perimeter is 20 feet

Perimeter = 20 ft
Final answer:

The perimeter of the heptagon is 20 feet

Applied rules:

• N-sided polygon rule: Perimeter = sum of all n sides

• Systematic addition: Add in order to avoid missing any sides

• Check your work: Count sides to ensure you didn't skip any

Rules and methods, laws,...
Perimeter = Side₁ + Side₂ + Side₃ + ... + Sideₙ
Perimeter of Irregular Shapes
Definition
Perimeter = Total Distance Around Shape
Distance around the outside edge
Method
Add All Side Lengths
Sum of every side measurement
Rule
Count Every Side Once
No side should be missed or double-counted
Key definitions:

Perimeter: The total length of the boundary of a 2D shape

Irregular shape: A shape with sides of different lengths and angles

Side: Each straight line segment that forms part of the boundary

Complete methodology:
  1. Trace the shape: Follow the outline with your finger to identify each side
  2. Label each side: Write down the length of each side as you go around
  3. Add systematically: Add all side lengths in order to avoid mistakes
  4. Check your work: Count sides again to ensure none were missed
Tip 1: Start at one corner and move clockwise or counterclockwise around the shape.
Tip 2: Mark each side as you count it to avoid double-counting or skipping.
Tip 3: Group numbers that add up to round numbers (like 5+5=10) to make mental math easier.
Tip 4: Always write the unit of measurement (cm, m, ft, etc.) in your final answer.
Common errors: Missing a side, counting a side twice, forgetting units, misreading measurements.
Memory aid: "Perimeter" starts with "P" like "Path" - think of walking around the path of the shape.
Formulas to know by heart:

• Perimeter of any shape: Add all side lengths

• Perimeter of rectangle: 2 × (length + width)

• Perimeter of square: 4 × side length

• Perimeter of triangle: side₁ + side₂ + side₃

Solution: Exercises 4 to 5
4 Composite shape
Exercise 4
Find the perimeter of this composite shape made of a rectangle and triangle:
Rectangle: length 8 cm, width 3 cm; Triangle sides: 5 cm, 5 cm, 8 cm (shared with rectangle)
Definition:

Composite shape: A shape made by combining two or more basic shapes. Only count the outer edges for perimeter.

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8cm
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3cm
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▲
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5cm
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5cm
8 + 3 + 5 + 5 + 3
=
24 cm
Step 1: Identify outer edges only

Don't count the shared side (8 cm base) twice. Count: 8 + 3 + 5 + 5 + 3

Step 2: Add the outer sides

8 + 3 + 5 + 5 + 3 = 24

Step 3: Include the unit

Perimeter = 24 cm

Perimeter = 24 cm
Final answer:

The perimeter of the composite shape is 24 cm

Applied rules:

• Outer edge rule: Only count the outside edges of composite shapes

• Shared sides: Don't count internal dividing lines

• Visual tracing: Trace the outside path with your finger

5 Complex figure
Exercise 5
Calculate the perimeter of this T-shaped figure:
Top bar: 6 units long, 2 units wide; Stem: 4 units long, 2 units wide (centered)
Definition:

T-shaped figure: A complex shape formed by two rectangles joined together. Count only the outer perimeter.

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6u
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2u
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2u
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4u
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6 + 2 + 2 + 4 + 2 + 2 + 2 + 4
=
24 units
Step 1: Trace the outer path

Start from top-left corner: right 6, down 2, right 2, down 4, left 2, down 2, left 2, up 4, left 2, up 4

Step 2: Organize the sides

Top: 6, Right sides: 2+4=6, Bottom: 2+2=4, Left sides: 2+4=6. Total: 6+6+4+6=24

Step 3: Verify the count

Count each unique outer edge to ensure accuracy: 8 sides total

Perimeter = 24 units
Final answer:

The perimeter of the T-shaped figure is 24 units

Applied rules:

• Continuous path: Follow the entire outer boundary without lifting your pencil

• Corner counting: At each corner, you turn 90 degrees to continue around

• Verification: Count the number of sides to ensure you haven't missed any

Key Rules, Methods, and Definitions for Perimeter of Irregular Shapes
Perimeter = Sum of All Side Lengths
Perimeter Formula
Key definitions:

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

Irregular shape: A shape with sides of different lengths and/or angles that are not all equal

Side length: The measurement of each straight edge of the shape

Unit of measurement: Standard measures like centimeters (cm), meters (m), inches (in), feet (ft), etc.

Complete methodology:
  1. Visual inspection: Look at the shape carefully and identify each distinct side
  2. Systematic approach: Start at one corner and move around the shape in order (clockwise or counterclockwise)
  3. Record measurements: Write down the length of each side as you encounter it
  4. Add systematically: Add all recorded side lengths together
  5. Check work: Count the number of sides to ensure none were missed or counted twice
Tip 1: Draw arrows along each side as you count it to avoid missing any.
Tip 2: Group numbers that make tens (like 7+3=10, 6+4=10) to make addition easier.
Tip 3: For complex shapes, break them into simpler parts mentally while tracking the outer edge.
Tip 4: Always double-check that your final answer includes the correct unit of measurement.
Tip 5: In composite shapes, only count the outermost edges, not internal dividing lines.
Common errors: Forgetting to include units, miscounting sides in complex figures, adding internal segments that aren't part of the perimeter, miscalculating addition.
Memory aids: "Perimeter" sounds like "fence" - you're measuring the fence around the shape. P=PATH around the shape.
Real-world applications: Fencing yards, framing pictures, laying borders around gardens, measuring trim for rooms.
Essential rules to remember:

• Rule 1: Perimeter = sum of ALL outer side lengths

• Rule 2: Only count sides that form the outer boundary

• Rule 3: All measurements must be in the same unit

• Rule 4: Order of addition doesn't matter (commutative property)

• Rule 5: Always include the unit in your final answer

• Rule 6: For composite shapes, exclude internal dividing lines

Examples: Rectangle P = 2(l+w), Square P = 4s, Triangle P = a+b+c
Special Cases
Problem-solving strategies:

• Strategy 1: Label each side with its measurement as you identify it

• Strategy 2: Use a consistent direction (clockwise/counterclockwise) when tracing the perimeter

• Strategy 3: Break complex shapes into recognizable parts

• Strategy 4: Estimate the answer first to check reasonableness

• Strategy 5: Re-trace the shape after calculating to verify all sides were included

Questions & Answers

Question: I sometimes get confused about which sides to count when finding the perimeter of a shape. How do I know which ones to include?

Answer: Great question! Here's how to determine which sides to count:

  • Only count the outer edges: These are the sides that form the boundary of the shape that you can trace with your finger.
  • Imagine walking around the shape: You would walk along the outside edge, not through the inside.
  • Look for the outline: The perimeter is the distance around the very edge of the shape.

For example, in a shape made of two rectangles joined together, you only count the outside edges, not the line where they're connected.

Tip: Start at one corner and trace around the shape with your finger, counting each side as you go. You'll end up back where you started!

Question: My child struggles with keeping track of which sides they've already counted in complex shapes. Any suggestions?

Answer: Here are some helpful strategies for keeping track:

  • Mark as you go: Have your child put a small checkmark or dot on each side as they count it.
  • Use a consistent direction: Always go clockwise or counterclockwise around the shape.
  • Draw arrows: Draw small arrows along each side in the direction they're counting.
  • Make a list: Write down each measurement as they encounter it: Side 1: ___, Side 2: ___, etc.

You can also encourage them to use their pencil to trace the perimeter slowly while counting aloud. This combines visual, tactile, and auditory learning.

Tip: Practice with simple shapes first, then gradually increase complexity as they build confidence.

Question: Why do we need to learn about perimeter? When will I ever use this in real life?

Answer: Perimeter calculations are used in many real-life situations! Here are some examples:

  • Fencing: If you want to fence your backyard, you need to know the perimeter to buy enough fencing material.
  • Gardening: Planning the border for a garden bed requires knowing the perimeter.
  • Carpentry: Building frames for doors, windows, or picture frames involves perimeter calculations.
  • Construction: Architects and builders use perimeter measurements for planning room layouts.
  • Art projects: Creating borders or frames for artwork requires perimeter knowledge.

Even in daily activities like determining how much ribbon you need for a gift box or how much paint you need for a room's trim, you're using perimeter concepts!