Solved Exercises on Finding Perimeter of Rectangle in Grade 3

Master finding perimeter of rectangles: basic formulas, real-life applications, geometric properties through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Basic rectangle
Exercise 1
Find the perimeter of a rectangle with length 6 units and width 4 units.
Definition:

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

Perimeter: The total distance around the rectangle

Length: The longer side of the rectangle

Width: The shorter side of the rectangle

Perimeter method:
  1. Add up all four sides: length + width + length + width
  2. Or use formula: Perimeter = 2 × (length + width)
Given
Length = 6, Width = 4
Formula
P = 2(l+w)
Result
P = 20
Step 1: Identify the dimensions

Length = 6 units, Width = 4 units

Step 2: Apply the perimeter formula

Perimeter = 2 × (length + width)

Perimeter = 2 × (6 + 4)

Step 3: Calculate the result

Perimeter = 2 × 10 = 20 units

Perimeter = 20 units
Final answer:

The perimeter of the rectangle is 20 units

Applied rules:

• Rectangle Property: Opposite sides are equal

• Perimeter Formula: P = 2(l+w) where l is length and w is width

• Order of Operations: Parentheses first, then multiplication

2 Square example
Exercise 2
Find the perimeter of a square with side length 5 units.
Definition:

Square: A special rectangle where all four sides are equal

Side: Any side of the square (all are equal)

Given
Side = 5 units
Formula
P = 4s
Result
P = 20
Step 1: Identify the dimensions

Since it's a square, all sides = 5 units

Length = 5 units, Width = 5 units

Step 2: Apply the perimeter formula

Method 1: P = 2(l + w) = 2(5 + 5) = 2(10) = 20

Method 2: P = 4s = 4(5) = 20 (since all sides are equal)

Step 3: Calculate the result

Perimeter = 20 units

Perimeter = 20 units
Final answer:

The perimeter of the square is 20 units

Applied rules:

• Square Property: All four sides are equal

• Square Perimeter: P = 4s where s is the side length

• Rectangle Perimeter: P = 2(l+w) also works for squares

3 Different dimensions
Exercise 3
Find the perimeter of a rectangle with length 8 units and width 3 units.
Definition:

Longer vs Shorter sides: Length is typically the longer side, width the shorter

Given
Length = 8, Width = 3
Formula
P = 2(l+w)
Result
P = 22
Step 1: Identify the dimensions

Length = 8 units, Width = 3 units

Step 2: Apply the perimeter formula

Perimeter = 2 × (length + width)

Perimeter = 2 × (8 + 3)

Step 3: Calculate the result

Perimeter = 2 × 11 = 22 units

Step 4: Verify with addition method

Perimeter = 8 + 3 + 8 + 3 = 22 units ✓

Perimeter = 22 units
Final answer:

The perimeter of the rectangle is 22 units

Applied rules:

• Rectangle Property: Opposite sides are equal

• Perimeter Formula: P = 2(l+w)

• Verification: Adding all four sides gives the same result

Rules and methods, laws,...
\(P = 2(l + w)\)
Perimeter of Rectangle
Rectangle
\(4 \text{ sides}, \text{opposite equal}\)
Properties
Perimeter
\(P = 2(l + w)\)
Rectangle formula
Square
\(P = 4s\)
All sides equal
Key definitions:

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

Perimeter: The total distance around the outside of a shape

Length: Usually the longer side of a rectangle

Width: Usually the shorter side of a rectangle

Side: Any edge of the rectangle

Complete methodology:
  1. Identify the shape: Confirm it's a rectangle
  2. Measure dimensions: Find the length and width
  3. Select formula: Use P = 2(l + w)
  4. Substitute values: Put the length and width into the formula
  5. Calculate: Perform the arithmetic
  6. Verify: Check by adding all four sides
Tip 1: Remember that opposite sides of a rectangle are equal.
Tip 2: A square is a special rectangle where all sides are equal.
Tip 3: You can always check by adding all four sides together.
Tip 4: Don't forget to include the unit of measurement in your answer.
Common errors: Forgetting to multiply by 2, confusing perimeter with area, misidentifying length vs width.
Memory aids: "Perimeter is the fence around the yard" and "add up all the sides".
Formulas to know by heart:

• Perimeter of rectangle: P = 2(l + w)

• Perimeter of square: P = 4s

• Area of rectangle: A = l × w

• Area of square: A = s²

Solution: Exercises 4 to 5
4 Real-world application
Exercise 4
A rectangular room has a length of 10 feet and a width of 8 feet. How much baseboard is needed to go around the walls?
Definition:

Word problem: A math problem presented in a real-world context

Baseboard: Trim that goes around the walls at floor level, which equals the perimeter

Given
Length = 10 ft, Width = 8 ft
Formula
P = 2(l+w)
Result
P = 36 ft
Step 1: Identify what's being asked

The problem asks for the amount of baseboard needed to go around the walls

This means we need to find the perimeter of the rectangular room

Step 2: Identify the dimensions

Room length = 10 feet, Room width = 8 feet

Step 3: Apply the perimeter formula

Perimeter = 2 × (length + width)

Perimeter = 2 × (10 + 8)

Step 4: Calculate the result

Perimeter = 2 × 18 = 36 feet

Step 5: State the answer in context

36 feet of baseboard is needed to go around the walls

Baseboard needed = 36 feet
Final answer:

36 feet of baseboard is needed to go around the walls

Applied rules:

• Real-world modeling: Representing physical situations with geometric concepts

• Perimeter application: Perimeter represents the distance around a shape

• Unit awareness: Including measurement units in the final answer

5 Comparison problem
Exercise 5
Rectangle A has length 7 cm and width 5 cm. Rectangle B has length 6 cm and width 6 cm. Which rectangle has a larger perimeter?
Definition:

Comparison problem: Calculating and comparing measurements of different shapes

Rectangle A: Standard rectangle with different length and width

Rectangle B: Actually a square since length = width

Rectangle A
P = 2(7+5) = 24cm
Rectangle B
P = 2(6+6) = 24cm
Result
Equal perimeters
Step 1: Calculate Rectangle A's perimeter

Rectangle A: length = 7 cm, width = 5 cm

Perimeter = 2 × (length + width) = 2 × (7 + 5) = 2 × 12 = 24 cm

Step 2: Calculate Rectangle B's perimeter

Rectangle B: length = 6 cm, width = 6 cm (this is actually a square)

Perimeter = 2 × (length + width) = 2 × (6 + 6) = 2 × 12 = 24 cm

Step 3: Compare the perimeters

Rectangle A: 24 cm

Rectangle B: 24 cm

24 cm = 24 cm

Step 4: State the conclusion

Both rectangles have the same perimeter of 24 cm

Both rectangles have equal perimeters (24 cm each)
Final answer:

Both rectangles have the same perimeter of 24 cm

Applied rules:

• Comparison strategy: Calculate both values before comparing

• Shape identification: Recognizing that Rectangle B is a square

• Units consistency: Both measurements in the same unit

Complete Guide: Laws, Methods, Rules, Definitions, Expressions
\(P = 2(l + w)\)
Perimeter of Rectangle
Key definitions:

Rectangle: A four-sided shape (quadrilateral) with opposite sides equal in length and all interior angles measuring 90° (right angles).

Perimeter: The total distance around the outside edge of a two-dimensional shape, measured in linear units.

Length: Typically the longer side of a rectangle, though this can vary depending on orientation.

Width: Typically the shorter side of a rectangle, though this can vary depending on orientation.

Side: Any of the four line segments that form the boundary of the rectangle.

Complete methodology:
  1. Identify the shape: Confirm that the figure is indeed a rectangle
  2. Measure or identify dimensions: Determine the length and width of the rectangle
  3. Select the appropriate formula: Use P = 2(l + w) for rectangles
  4. Substitute values: Replace l (length) and w (width) with their actual measurements
  5. Perform calculations: Add length and width, then multiply by 2
  6. State the answer: Include the appropriate unit of measurement
  7. Verify the result: Optionally add all four sides to confirm the answer
Tip 1: Remember that rectangles have two pairs of equal sides. If you know the length and width, you automatically know all four sides.
Tip 2: A square is a special type of rectangle where all four sides are equal. You can use either P = 2(l + w) or P = 4s for squares.

Tip 3: Always include the unit of measurement (inches, feet, centimeters, etc.) in your final answer.
Tip 4: You can check your answer by adding all four sides individually: length + width + length + width.
Rectangle Properties: 4 right angles, opposite sides equal, diagonals equal and bisect each other, sum of interior angles is 360°.
Perimeter Characteristics: Measures the boundary of a shape, always a linear measurement, expressed in units like inches, feet, or centimeters.
Common Errors: Confusing perimeter with area, forgetting to multiply by 2 in the formula, misidentifying length vs width.
Essential formulas:

• Perimeter of rectangle: P = 2(l + w)

• Perimeter of square: P = 4s

• Area of rectangle: A = l × w

• Area of square: A = s²

• Diagonal of rectangle: d = √(l² + w²)

Rectangle Perimeter Guide
📏
Rectangle Structure

• 4 sides: 2 lengths (l) + 2 widths (w)

• 4 right angles (90°)

• Opposite sides equal

• Perimeter = 2(l + w)

Perimeter Calculation

• Method 1: Add all sides

• Method 2: P = 2(l + w)

• For squares: P = 4s

• Units: same as side measurements

Verification

• Add all 4 sides: l + w + l + w

• Should equal 2(l + w)

• Check arithmetic carefully

• Include units in answer

Problem-Solving Workflow
1
Identify Shape
2
Get Dimensions
3
Apply Formula
4
Calculate
5
Verify Answer
Visual Representation

Rectangle with length (l) and width (w)

Perimeter = distance around the rectangle

P = 2(l + w) = l + w + l + w

Remember: Perimeter measures the boundary of the rectangle!

Questions & Answers

Question: What's the difference between perimeter and area? I always get them mixed up.

Answer: This is a very common question! Here's the key difference:

  • Perimeter: The distance around the outside of a shape. Think of it as walking around the edge of a garden. It's measured in linear units (inches, feet, centimeters).
  • Area: The amount of space inside a shape. Think of it as covering the floor with tiles. It's measured in square units (square inches, square feet, square centimeters).

For a rectangle: Perimeter = 2(length + width) [linear measurement] Area = length × width [square measurement]

A helpful memory trick: "Perimeter" starts with "P" like "Periscope" - you're looking around the edge. "Area" sounds like "are" - "How much area is covered?"

Question: Why do we multiply by 2 in the perimeter formula? Can't we just add the length and width once?

Answer: Great question! We multiply by 2 because a rectangle has TWO lengths and TWO widths. Let's break it down:

  • A rectangle has 4 sides: top, bottom, left, right
  • The top and bottom sides are both equal to the length
  • The left and right sides are both equal to the width
  • So the total perimeter is: length + length + width + width = 2×length + 2×width = 2(length + width)

If you only added length + width, you'd only be counting half the perimeter! For example, if length = 4 and width = 3: Using P = l + w: 4 + 3 = 7 (incorrect!) Using P = 2(l + w): 2(4 + 3) = 2(7) = 14 (correct!)

You can verify: 4 + 3 + 4 + 3 = 14 ✓

Question: Is a square really a rectangle? I thought they were different shapes.

Answer: Yes, a square IS a special type of rectangle! Here's why:

  • A rectangle is defined as a four-sided shape with all angles equal to 90° (right angles)
  • A square meets this definition: it has four sides and all four angles are 90°
  • But a square has an extra property: all four sides are equal in length

Think of it this way: all squares are rectangles, but not all rectangles are squares. It's like how all dogs are animals, but not all animals are dogs.

This is why the rectangle perimeter formula P = 2(l + w) works for squares too. If all sides are equal (let's call that length 's'), then P = 2(s + s) = 2(2s) = 4s, which is the square perimeter formula!