Solved Exercises on Area Word Problems in Grade 3

Master area calculations: rectangles, squares, real-world applications through these 5 detailed exercises with step-by-step solutions.

Solution: Exercises 1 to 3
1 Rectangle Area
Exercise 1
Sarah has a rectangular garden that is 8 feet long and 5 feet wide. What is the area of her garden?
Definition:

Area: The amount of space inside a shape measured in square units

Rectangle: A 4-sided shape with 4 right angles and opposite sides equal

Area calculation method:
  1. Identify the length and width of the rectangle
  2. Apply the formula: Area = Length × Width
  3. Multiply the numbers together
  4. Add the square unit (e.g., square feet)
Area = Length × Width
Rectangle Area Formula
Step 1: Identify the dimensions

Length = 8 feet, Width = 5 feet

Step 2: Apply the formula

Area = Length × Width = 8 × 5

Step 3: Calculate

8 × 5 = 40

Step 4: Add units

Area = 40 square feet

8 ft × 5 ft = 40 sq ft

Area = 40 square feet
Final answer:

The area of Sarah's garden is 40 square feet.

Applied rules:

• Formula: Area = Length × Width

• Units: Always include square units in your answer

• Multiplication: Multiply the length by the width

2 Square Area
Exercise 2
Tom has a square sandbox with each side measuring 6 feet. What is the area of the sandbox?
Definition:

Square: A rectangle with all 4 sides equal in length

All sides equal: Length = Width in a square

Area = Side × Side = Side²
Square Area Formula
Step 1: Identify the side length

Side = 6 feet

Step 2: Apply the formula

Area = Side × Side = 6 × 6

Step 3: Calculate

6 × 6 = 36

Step 4: Add units

Area = 36 square feet

6 ft × 6 ft = 36 sq ft

Area = 36 square feet
Final answer:

The area of Tom's sandbox is 36 square feet.

Applied rules:

• Formula: Area = Side × Side = Side²

• Equality: All sides of a square are equal

• Squaring: Multiplying a number by itself

3 Real-world Application
Exercise 3
A rectangular room is 10 feet long and 8 feet wide. If carpet costs $2 per square foot, how much will it cost to carpet the entire room?
Definition:

Real-world application: Using area to solve practical problems involving cost, materials, or space

Multi-step problem solving:
  1. Calculate the area of the room
  2. Determine the cost per square unit
  3. Multiply area by cost per unit
  4. Include currency in final answer
Step 1: Find the area of the room

Area = Length × Width = 10 × 8 = 80 square feet

Step 2: Identify the cost per square foot

Cost = $2 per square foot

Step 3: Calculate total cost

Total Cost = Area × Cost per square foot = 80 × $2 = $160

Step 4: State the final answer

It will cost $160 to carpet the room

10 ft × 8 ft = 80 sq ft

80 sq ft × $2/sq ft = $160

Total cost = $160
Final answer:

It will cost $160 to carpet the entire room.

Applied rules:

• Area calculation: First find the area using Area = Length × Width

• Multiplication: Multiply area by cost per unit

• Real-world context: Apply mathematical concepts to practical situations

Area Rules, Laws, and Methods
Area = Length × Width
Rectangle Area Formula
Square Area
Area = Side × Side
When all sides are equal
Unit Conversion
1 foot = 12 inches
Convert units if needed
Square Units
feet², inches², cm²
Always use square units
Key definitions:

Area: The amount of space inside a 2-dimensional shape

Rectangle: A 4-sided shape with 4 right angles

Square: A rectangle with all 4 sides equal

Square unit: Area measurement (square feet, square inches, etc.)

Area calculation methodology:
  1. Identify the shape: Determine if it's a rectangle, square, or other polygon
  2. Measure dimensions: Find the length and width (or sides)
  3. Apply formula: Use the appropriate area formula
  4. Calculate: Multiply the dimensions
  5. Include units: Always express area in square units
Tip 1: Count squares on grid paper to visualize area.
Tip 2: Remember that area is always measured in square units.
Tip 3: Check your work by counting unit squares if available.
Tip 4: Draw a picture to help visualize the problem.
Common errors: Forgetting square units, mixing up length and width, miscalculating multiplication.
Key concepts: Area measures space inside, length × width = area, square units for area.
Formulas to know by heart:

• Rectangle area: Length × Width

• Square area: Side × Side

• Always use square units for area

• Area measures the inside of a shape

Area Calculation Infographic

📐
Shape Identification

Rectangle: 4 sides, 4 right angles, opposite sides equal

Square: 4 equal sides, 4 right angles

Formula Application

Rectangle: Area = Length × Width

Square: Area = Side × Side

Measurement

Measure length and width in same units

Convert units if necessary

Units

Area always in square units

Examples: sq ft, sq in, sq cm

Area Calculation Steps
1
Identify Shape
2
Measure Sides
3
Apply Formula
4
Calculate
5
Add Units
Visual Representation
🟦 8×5=40 sq units
⬜ 6×6=36 sq units
🟩 10×8=80 sq units
Practice Makes Perfect! 💪
Solution: Exercises 4 to 5
4 Painting Project
Exercise 4
A rectangular wall is 12 feet long and 9 feet tall. One gallon of paint covers 36 square feet. How many gallons of paint are needed to cover the entire wall?
Definition:

Coverage problem: Calculating how many units of material are needed based on area and coverage rate

Multi-step problem solving:
  1. Calculate the area of the wall
  2. Determine the coverage rate per unit
  3. Divide total area by coverage rate
  4. Round up if there's a remainder
Step 1: Find the area of the wall

Area = Length × Height = 12 × 9 = 108 square feet

Step 2: Identify the coverage rate

One gallon covers 36 square feet

Step 3: Calculate gallons needed

Gallons = Total Area ÷ Coverage per gallon = 108 ÷ 36 = 3 gallons

Step 4: State the final answer

3 gallons of paint are needed

12 ft × 9 ft = 108 sq ft

108 sq ft ÷ 36 sq ft/gallon = 3 gallons

Paint needed = 3 gallons
Final answer:

3 gallons of paint are needed to cover the entire wall.

Applied rules:

• Area calculation: Area = Length × Height

• Division: Divide total area by coverage rate

• Real-world context: Apply division to determine quantity needed

5 Garden Planning
Exercise 5
Maria wants to plant flowers in a rectangular garden bed that is 7 feet long and 4 feet wide. Each flower needs 1 square foot of space. How many flowers can she plant in the garden bed?
Definition:

Space allocation: Determining how many items fit in a given area based on space requirements per item

Space allocation method:
  1. Calculate the total area available
  2. Determine space required per item
  3. Divide total area by space per item
  4. Round down if there's a remainder
Step 1: Find the area of the garden bed

Area = Length × Width = 7 × 4 = 28 square feet

Step 2: Identify space needed per flower

Each flower needs 1 square foot

Step 3: Calculate number of flowers

Number of flowers = Total Area ÷ Space per flower = 28 ÷ 1 = 28 flowers

Step 4: State the final answer

Maria can plant 28 flowers

7 ft × 4 ft = 28 sq ft

28 sq ft ÷ 1 sq ft/flower = 28 flowers

Flowers = 28
Final answer:

Maria can plant 28 flowers in the garden bed.

Applied rules:

• Area calculation: Area = Length × Width

• Division: Divide total area by space requirement

• Practical constraint: Cannot plant partial flowers

Area Word Problems - Comprehensive Guide
Area = Length × Width
Area Formula
Key definitions:

Area: The measure of the surface inside a 2-dimensional shape

Rectangle: A quadrilateral with four right angles and opposite sides equal

Square: A rectangle with all four sides equal in length

Square unit: Unit of measurement for area (square feet, square inches, etc.)

Step-by-step area problem solving:
  1. Read the problem carefully: Identify what shape is involved
  2. Find the dimensions: Locate length and width measurements
  3. Choose the formula: Rectangle: A = L × W, Square: A = S × S
  4. Calculate: Multiply the dimensions
  5. Check units: Ensure answer is in square units
  6. Answer the question: State the final answer in context
Tip 1: Draw a picture of the shape to visualize the problem.
Tip 2: Always include square units in your final answer.
Tip 3: In real-world problems, round up when calculating materials.
Tip 4: Use grid paper to count squares when learning area.
Common errors: Forgetting square units, confusing perimeter with area, multiplying wrong dimensions.
Success strategies: Always draw a diagram, check units, reread the question.
Essential area formulas:

• Rectangle: Area = Length × Width

• Square: Area = Side × Side

• Area is always measured in square units

• Area measures the inside of a shape

Area Problem Solving

📏
Problem Types

• Find area given dimensions

• Find dimensions given area

• Real-world applications

• Multi-step problems

Common Mistakes

• Forgetting square units

• Adding instead of multiplying

• Confusing length and width

• Not reading units carefully

Success Tips

• Always draw a picture

• Label dimensions

• Write the formula

• Check your answer

Key Reminders

• Area = Length × Width

• Square units only

• Measures inside shape

• Practice regularly

Problem Solving Process
1
Read Carefully
2
Draw Diagram
3
Identify Formula
4
Calculate
5
Check Answer
Area Examples
🟦 8×5=40 sq ft
⬜ 6×6=36 sq ft
🟩 10×8=80 sq ft
🟨 7×4=28 sq ft
Master Area Problems! 🎯

Questions & Answers

Question: I don't understand why we multiply length and width to find area. Why can't we just add them together?

Answer: Great question! Area measures how much space is inside a shape, not the distance around it. Let me explain with a visual:

Think of a rectangle that is 3 feet long and 2 feet wide. If you draw this on grid paper, you'll see it covers 6 little squares. That's 3 rows of 2 squares each, which is 3 × 2 = 6 squares.

If you added length + width (3 + 2 = 5), you'd get 5, but the rectangle actually covers 6 squares, not 5! When we multiply length × width, we're counting all the square units that fit inside.

Adding would only give us part of the story - multiplication gives us the complete count of all the tiny squares that fill the shape!

Question: When do I know if I need to find area or perimeter in a word problem?

Answer: Look for clue words in the problem!

Area clues: words like "cover," "carpet," "paint," "floor," "space," "inside," "fill," "garden," "field," "how much space."

Perimeter clues: words like "fence," "border," "around," "edge," "surround," "go around," "walk around," "trim," "frame," "distance around."

For example: "How much carpet do I need?" = AREA (covering the floor)

"How much fencing do I need?" = PERIMETER (going around the edge)

Always ask yourself: "Am I filling the inside or going around the outside?"

Question: My child gets confused about when to use square units. How can I help them remember?

Answer: Here are some helpful strategies to help your child remember square units:

  • Create a memory phrase: "Area is square - always add 'square' before the unit!"
  • Visual connection: Show them that area covers squares inside the shape, so we say "square feet," "square inches," etc.
  • Practice with manipulatives: Use tiles, blocks, or grid paper to physically count the squares being covered.
  • Make it routine: Every time they calculate area, have them write "square units" as part of their answer automatically.

You can also create a simple rule: "If it's area, it's always square _____" where the blank is filled with the unit of measurement.

Consistent practice with this pattern will help make it automatic for your child!