Practice Questions on Perimeter of Irregular Shapes with Missing Sides in Grade 3

Master perimeter calculations: irregular shapes with missing sides, step-by-step solutions, rules, methods, and practice questions through these 5 detailed exercises.

Solution: Questions 1 to 3
1 L-Shape with Missing Side
Question 1
Find the perimeter of an L-shaped figure with sides measuring:
Top horizontal: 8 cm
Right vertical: 5 cm
Bottom horizontal: 12 cm
Left vertical: 3 cm
Middle horizontal: 4 cm
Middle vertical: ? (missing)
Hint: Opposite sides of rectangles are equal.
Definition:

Perimeter: The total distance around the outside of a shape

Missing side: A side whose length needs to be calculated from given information

Opposite sides: In rectangles, parallel sides have equal lengths

Finding missing sides method:
  1. Look for relationships between known sides
  2. Use geometric properties (opposite sides equal)
  3. Calculate the missing measurement
  4. Add all sides to find perimeter
Find missing side
5 - 3 = 2 cm
All sides
8+5+12+3+4+2
Sum
34 cm
Step 1: Identify the missing side

Looking at the L-shape, the middle vertical side can be found by: Right vertical - Left vertical = 5 - 3 = 2 cm

Step 2: Add all measurements

8 + 5 + 12 + 3 + 4 + 2 = 34

Step 3: State the unit

Total perimeter = 34 cm

Perimeter = 34 cm
Final answer:

The perimeter of the L-shaped figure is 34 cm

Applied rules:

• Rectangle property: Opposite sides are equal

• Missing side rule: Use known sides to calculate unknown ones

• Perimeter Rule: Sum of all outer sides

• Measurement: Include units in final answer

8 cm 5 cm 12 cm 3 cm 4 cm ? cm
2 Rectangle with Cutout
Question 2
Find the perimeter of a rectangle that is 10 cm × 6 cm with a smaller rectangle cut out from one corner. The cutout measures 3 cm × 2 cm. One side of the cutout is missing from the drawing.
Definition:

Rectangle cutout: A smaller rectangle removed from a larger rectangle

Internal perimeter: The perimeter of the cutout that becomes part of the total perimeter

Large rectangle
10+6+10+6
Cutout
3+2+3+2
Total
32+10=42 cm
Step 1: Calculate large rectangle perimeter

10 + 6 + 10 + 6 = 32 cm

Step 2: Calculate cutout perimeter

3 + 2 + 3 + 2 = 10 cm

Step 3: Add both perimeters

32 + 10 = 42 cm

Step 4: Verify no sides missed

All sides of large rectangle and cutout counted

Perimeter = 42 cm
Final answer:

The perimeter of the rectangle with cutout is 42 cm

Applied rules:

• Cutout rule: Internal cutouts add to the total perimeter

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

• Perimeter addition: Sum all outer and inner boundaries

• Unit consistency: All measurements in same unit

10 cm 6 cm 3 cm 2 cm
3 T-Shape with Missing Dimensions
Question 3
Find the perimeter of a T-shaped figure. The top bar is 8 cm long and 2 cm wide. The vertical stem is 2 cm wide and 6 cm tall. The connection part has a missing dimension: ? cm. Use the fact that opposite sides of rectangles are equal.
Definition:

T-Shape: A compound shape made of two rectangles joined together

Top bar sides
8+2+8+2
Stem sides
6+2+6+2
Adjustment
Subtract overlapping parts
Step 1: Calculate top bar perimeter

8 + 2 + 8 + 2 = 20 cm

Step 2: Calculate stem perimeter

6 + 2 + 6 + 2 = 16 cm

Step 3: Account for connection

Where they connect, subtract 2 × 2 = 4 cm (connection width counted twice)

Step 4: Calculate total perimeter

20 + 16 - 4 = 32 cm

Perimeter = 32 cm
Final answer:

The perimeter of the T-shaped figure is 32 cm

Applied rules:

• Compound shapes: Include all outer boundaries

• Connection rule: Subtract overlapping internal segments

• Rectangle property: Opposite sides are equal

• Accurate measurement: Count every side segment once

8 cm 2 cm 6 cm 2 cm
Key Concepts: Rules, Laws, and Methods
Perimeter = Sum of all sides
Basic Formula
Rule 1
P = s₁ + s₂ + s₃ + ... + sₙ
Sum of all side lengths
Rule 2
Missing side = Known opposite side
Rectangle property
Rule 3
P = 2(l + w)
Rectangle perimeter
Key definitions:

Perimeter: Distance around the outside of a shape

Irregular Shape: Shape with unequal sides and angles

Missing Side: A side whose length must be calculated from given information

Rectangle Property: Opposite sides of rectangles are equal

Compound Shape: A shape made of multiple simpler shapes

Complete methodology:
  1. Identify missing sides: Look for unlabeled sides
  2. Find relationships: Use geometric properties to calculate missing measurements
  3. Write down all sides: List all the side lengths including calculated ones
  4. Add all measurements: Sum all the side lengths
  5. Check your work: Ensure all sides are accounted for
  6. Write the answer: Don't forget to put the units (cm, m, etc.)
Tip 1: Look for rectangles within the shape - opposite sides are equal.
Tip 2: If two parallel sides are shown, one might help find the other.
Tip 3: Look for sides that together make up another known side.
Tip 4: Always include units in your final answer.
Tip 5: Draw the shape and label all known sides first.
Common errors: Forgetting to calculate missing sides, double-counting shared sides, missing internal boundaries.
Problem-solving tips: Look for geometric relationships, use rectangle properties, verify your answer.
Essential formulas to remember:

• Perimeter of any shape: P = sum of all sides

• Rectangle: P = 2(length + width)

• Square: P = 4 × side

• Missing side: Use geometric relationships (opposite sides equal)

Visual Guide: Perimeter Patterns with Missing Sides
Understanding Perimeter Relationships
Visual comparison of different irregular shapes with missing sides and their perimeter calculations:
Shape A: L-shape with missing side
Shape B: Rectangle with cutout
Shape C: T-shape with connections

Analysis: The chart shows how missing sides affect perimeter calculations.

  • Missing sides require calculation from known sides
  • Cutouts add to the perimeter
  • Connections may require adjustments
Solution: Questions 4 to 5
4 U-Shape with Missing Dimensions
Question 4
Find the perimeter of a U-shaped figure. The outer rectangle is 12 cm × 8 cm. The inner cutout rectangle is 6 cm × 4 cm. Two connecting sides are missing and need to be calculated. Use rectangle properties to find the missing measurements.
Definition:

U-Shape: A rectangle with a rectangular cutout that leaves a U-shaped figure

Outer sides
12+8+12+8
Inner sides
6+4+6+4
Total
40+20=60 cm
Step 1: Calculate outer rectangle perimeter

12 + 8 + 12 + 8 = 40 cm

Step 2: Calculate inner rectangle perimeter

6 + 4 + 6 + 4 = 20 cm

Step 3: Add both perimeters

40 + 20 = 60 cm

Step 4: State the answer

Total perimeter = 60 cm

Perimeter = 60 cm
Final answer:

The perimeter of the U-shaped figure is 60 cm

Applied rules:

• Cutout rule: Internal cutouts add to the total perimeter

• Rectangle property: Opposite sides are equal

• Compound shapes: Include all outer and inner boundaries

• Attention to detail: Account for all parts of the shape

12 cm 8 cm 6 cm 4 cm
5 Complex Shape with Multiple Missing Sides
Question 5
Find the perimeter of a complex shape made of three connected rectangles. Given measurements: top rectangle is 5 cm × 3 cm, middle rectangle is 7 cm × 2 cm, bottom rectangle is 5 cm × 4 cm. Several connecting sides are missing. Use the fact that the top and bottom rectangles are aligned and have the same width.
Definition:

Complex shape: A shape composed of multiple rectangles joined together

Top rectangle
5+3+5+3
Middle rectangle
7+2+7+2
Bottom rectangle
5+4+5+4
Step 1: Calculate top rectangle perimeter

5 + 3 + 5 + 3 = 16 cm

Step 2: Calculate middle rectangle perimeter

7 + 2 + 7 + 2 = 18 cm

Step 3: Calculate bottom rectangle perimeter

5 + 4 + 5 + 4 = 18 cm

Step 4: Account for connections

Where rectangles connect, subtract internal sides: 2 × 2 = 4 cm

Step 5: Calculate total perimeter

16 + 18 + 18 - 4 = 48 cm

Perimeter = 48 cm
Final answer:

The perimeter of the complex shape is 48 cm

Applied rules:

• Compound rule: Add perimeters of individual shapes

• Connection rule: Subtract overlapping internal segments

• Rectangle property: Opposite sides are equal

• Pattern recognition: Look for alignment and equality

5 cm 3 cm 7 cm 2 cm 5 cm 4 cm
Comprehensive Guide: Laws, Methods, Rules, Definitions
P = s₁ + s₂ + s₃ + ... + sₙ (with missing sides calculated)
Perimeter Formula
Key definitions:

Perimeter: Total distance around the boundary of a 2D shape

Irregular Shape: Polygon with sides of different lengths and/or angles

Missing Side: A side length that must be determined from other given measurements

Rectangle Property: Opposite sides of a rectangle are equal in length

Compound Shape: A shape made by combining multiple simpler shapes

Internal Boundary: A boundary inside the shape that contributes to the perimeter

Complete methodology:
  1. Shape Analysis: Identify all visible sides and missing sides
  2. Relationship Discovery: Look for geometric relationships to find missing measurements
  3. Side Calculation: Use properties like "opposite sides equal" to calculate missing lengths
  4. Boundary Tracing: Follow the outer edge systematically
  5. Summation: Add all side lengths together
  6. Unit Application: Express result with proper units
  7. Verification: Check that all sides have been accounted for
Tip 1: Look for rectangles within the shape - opposite sides are always equal

Tip 2: If two parts of a side are shown, add them to get the full side

Tip 3: Parallel sides often have relationships you can use

Tip 4: Draw the shape and label known sides first

Tip 5: Check your answer by making sure it makes sense

Tip 6: Remember that cutouts add to the perimeter, not subtract

Common errors: Forgetting to calculate missing sides, double-counting shared sides, ignoring internal boundaries, misapplying rectangle properties.

Missing side strategies: Use opposite sides equality, look for parts that sum to known sides, apply rectangle properties.

Essential formulas and rules:

• General perimeter: P = sum of all side lengths

• Rectangle: P = 2(length + width)

• Square: P = 4 × side length

• Triangle: P = side₁ + side₂ + side₃

• Rectangle property: Opposite sides are equal

• Compound shapes: P = sum of all outer boundaries including internal cutouts

Special cases: For shapes with cutouts, include both outer and inner boundaries. For connected rectangles, account for shared sides appropriately.

Problem-solving strategies: Identify rectangles, use opposite sides equality, break complex shapes into parts.

Questions & Answers

Question: How do I know which sides are missing and how to find them?

Answer: Great question! Here's how to identify and find missing sides:

  • Look for unlabeled sides: Any side without a measurement label might be missing
  • Find rectangles: Look for rectangular parts of the shape
  • Use rectangle property: Opposite sides of rectangles are equal
  • Look for relationships: Two parts of a side may add up to a known side

Example: If you see a rectangle with one long side labeled 8 cm, the opposite long side is also 8 cm. If you see two segments that together make up a side, add them to get the total length.

Always look for geometric patterns and relationships in the shape.

Question: My child is confused about when to add and when to subtract sides in complex shapes. Can you explain?

Answer: Here are the key principles for adding and subtracting sides:

  • Add all sides: Count every outer boundary of the shape
  • Add internal boundaries: Cutouts and holes add to the perimeter
  • Subtract overlaps: When shapes connect, subtract the shared internal segments
  • Don't double-count: Shared sides between connected shapes are counted once

Think of perimeter as the path you would walk around the outside of the shape. You walk along all outer edges and around any internal holes, but you don't walk along shared boundaries inside the shape twice.

Practice with simple shapes first, then move to more complex ones.

Question: What's the best way to teach students to recognize rectangle properties in complex shapes?

Answer: Here are effective teaching strategies for recognizing rectangle properties:

  • Highlight rectangles: Use different colors to outline rectangular sections
  • Label systematically: Mark opposite sides with the same symbol
  • Visual demonstrations: Show that opposite sides are parallel and equal
  • Hands-on activities: Use manipulatives to build and deconstruct shapes
  • Pattern recognition: Practice identifying rectangles in various orientations

Emphasize that even when rectangles are part of larger shapes, their fundamental properties (opposite sides equal, all angles 90 degrees) remain true. Encourage students to mentally "break apart" complex shapes into simpler rectangles to identify relationships.

Repetition with varied examples helps students develop this recognition skill.