Solved Exercises on Finding Perimeter of Rectangle Calculator in Grade 3

Master finding perimeter of rectangles with calculator tools: 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 7 units and width 4 units using a calculator.
Definition:

Calculator: A tool that helps perform mathematical operations quickly and accurately

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

Perimeter: The total distance around the rectangle

Calculator method:
  1. Enter the length: 7
  2. Press the + button
  3. Enter the width: 4
  4. Press the = button (to get length + width)
  5. Press the × button
  6. Enter 2
  7. Press = to get the final result
Given
Length = 7, Width = 4
Formula
P = 2(l+w)
Result
P = 22
Step 1: Identify the dimensions

Length = 7 units, Width = 4 units

Step 2: Apply the perimeter formula

Perimeter = 2 × (length + width)

Perimeter = 2 × (7 + 4)

Step 3: Calculate with calculator

First: 7 + 4 = 11

Then: 2 × 11 = 22

Step 4: Verify the result

Calculator shows: 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) where l is length and w is width

• Calculator Operation: Following order of operations with calculator

2 Square example
Exercise 2
Find the perimeter of a square with side length 6 units using a calculator.
Definition:

Square: A special rectangle where all four sides are equal

Calculator Method: Using 4 × side for squares

Given
Side = 6 units
Formula
P = 4s
Result
P = 24
Step 1: Identify the dimensions

Since it's a square, all sides = 6 units

Length = 6 units, Width = 6 units

Step 2: Calculator operation for square

Method 1: P = 4 × side = 4 × 6 = 24

Method 2: P = 2(l + w) = 2(6 + 6) = 2(12) = 24

Step 3: Enter on calculator

Press: 4 × 6 =

Calculator shows: 24

Step 4: Verify with rectangle formula

Press: 2 × (6 + 6) =

Calculator shows: 24 ✓

Perimeter = 24 units
Final answer:

The perimeter of the square is 24 units

Applied rules:

• Square Property: All four sides are equal

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

• Calculator Efficiency: Using the simplest formula reduces steps

3 Larger numbers
Exercise 3
Find the perimeter of a rectangle with length 15 units and width 8 units using a calculator.
Definition:

Large Numbers: Numbers that are difficult to calculate mentally

Calculator Benefit: Accuracy and efficiency with large numbers

Given
Length = 15, Width = 8
Formula
P = 2(l+w)
Result
P = 46
Step 1: Identify the dimensions

Length = 15 units, Width = 8 units

Step 2: Apply the perimeter formula

Perimeter = 2 × (length + width)

Perimeter = 2 × (15 + 8)

Step 3: Calculate with calculator

First: 15 + 8 = 23

Then: 2 × 23 = 46

Step 4: Verify with addition method

Calculator: 15 + 8 + 15 + 8 = 46 ✓

Perimeter = 46 units
Final answer:

The perimeter of the rectangle is 46 units

Applied rules:

• Rectangle Property: Opposite sides are equal

• Perimeter Formula: P = 2(l+w)

• Calculator Advantage: Accuracy with larger numbers

Rules and methods, laws,...
\(P = 2(l + w)\)
Perimeter of Rectangle with Calculator
Rectangle
\(P = 2(l + w)\)
Basic formula
Square
\(P = 4s\)
Special case
Calculator
\(P = 2(l+w)\)
Efficient method
Key definitions:

Calculator: An electronic device that performs mathematical operations quickly and accurately

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. Enter on calculator: Input the numbers and operations
  5. Calculate: Press the equals button
  6. Verify: Check by adding all four sides
Tip 1: Use calculator for accuracy with large numbers.
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 12 feet and a width of 10 feet. How much baseboard is needed to go around the walls? Use a calculator to find the answer.
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 = 12 ft, Width = 10 ft
Formula
P = 2(l+w)
Result
P = 44 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 = 12 feet, Room width = 10 feet

Step 3: Apply the perimeter formula

Perimeter = 2 × (length + width)

Perimeter = 2 × (12 + 10)

Step 4: Calculate with calculator

First: 12 + 10 = 22

Then: 2 × 22 = 44

Step 5: State the answer in context

44 feet of baseboard is needed to go around the walls

Baseboard needed = 44 feet
Final answer:

44 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 14 cm and width 6 cm. Rectangle B has length 12 cm and width 8 cm. Which rectangle has a larger perimeter? Use a calculator to find both perimeters.
Definition:

Comparison problem: Calculating and comparing measurements of different shapes

Calculator efficiency: Using calculator to handle multiple calculations

Rectangle A
P = 2(14+6) = 40cm
Rectangle B
P = 2(12+8) = 40cm
Result
Equal perimeters
Step 1: Calculate Rectangle A's perimeter with calculator

Rectangle A: length = 14 cm, width = 6 cm

Calculator: 14 + 6 = 20, then 2 × 20 = 40

Perimeter = 40 cm

Step 2: Calculate Rectangle B's perimeter with calculator

Rectangle B: length = 12 cm, width = 8 cm

Calculator: 12 + 8 = 20, then 2 × 20 = 40

Perimeter = 40 cm

Step 3: Compare the perimeters

Rectangle A: 40 cm

Rectangle B: 40 cm

40 cm = 40 cm

Step 4: State the conclusion

Both rectangles have the same perimeter of 40 cm

Both rectangles have equal perimeters (40 cm each)
Final answer:

Both rectangles have the same perimeter of 40 cm

Applied rules:

• Comparison strategy: Calculate both values before comparing

• Calculator utility: Handling multiple calculations efficiently

• Units consistency: Both measurements in the same unit

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

Calculator: An electronic device that performs mathematical operations quickly and accurately.

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. Enter values on calculator: Input the numbers and operations in the correct sequence
  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°.
Calculator Benefits: Accuracy with large numbers, speed, reduces calculation errors.
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 Calculator Guide
🧮
Rectangle Structure

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

• 4 right angles (90°)

• Opposite sides equal

• Perimeter = 2(l + w)

Calculator Steps

• Enter length

• Press +

• Enter width

• Press =

• Press ×

• Enter 2

• Press =

Verification

• Add all 4 sides: l + w + l + w

• Should equal 2(l + w)

• Check calculator result

• Include units in answer

Calculator Problem Solving
1
Identify Shape
2
Get Dimensions
3
Select Formula
4
Enter Calculator
5
Calculate & Verify
Visual Representation

Rectangle with length (l) and width (w)

Perimeter = distance around the rectangle

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

Remember: Calculator helps with accuracy!

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!