Area Word Problems | Solved Exercises

Solution: Exercises 1 to 3

1 Basic area word problem

Exercise 1

A rectangular garden is 6 feet long and 4 feet wide. What is the area of the garden?

Definition:

Area word problem: A mathematical problem presented in sentence form that requires finding the area of a shape

Word problem method:

Read the problem carefully
Identify the dimensions (length and width)
Apply the area formula: Area = Length × Width
State the answer in square units

Length

6 feet

Width

4 feet

Area

6 × 4 = 24

Step 1: Identify the dimensions

Length = 6 feet, Width = 4 feet

Step 2: Apply the area formula

Area = Length × Width = 6 × 4

Step 3: Calculate the area

Area = 24 square feet

Final answer:

The area of the garden is 24 square feet

Applied rules:

• Area formula: Area = Length × Width

• Multiplication: 6 × 4 = 24

• Area units: Always express in square units

2 Area comparison word problem

Exercise 2

Sarah's bedroom is 8 feet by 7 feet. Tom's bedroom is 9 feet by 6 feet. Whose bedroom has the larger area?

Definition:

Area comparison problem: A word problem that requires calculating areas and comparing them

Sarah's Area

8 × 7 = 56

Tom's Area

9 × 6 = 54

Comparison

56 > 54

Step 1: Calculate Sarah's bedroom area

Area = 8 × 7 = 56 square feet

Step 2: Calculate Tom's bedroom area

Area = 9 × 6 = 54 square feet

Step 3: Compare the areas

56 > 54, so Sarah's bedroom is larger

Area Word Problems | Solved Exercises | Mathematics Grade 3

Solution: Exercises 1 to 3

1 Rectangle area problem

Exercise 1

A rectangular garden is 6 feet long and 4 feet wide. What is the area of the garden?

Definition:

Area word problem: A problem that requires calculating area using information presented in sentence form

Problem-solving method:

Read the problem carefully and identify what is being asked
Identify the dimensions (length and width)
Apply the area formula: Area = Length × Width
Calculate and state the answer with units

Length

6 feet

Width

4 feet

Area

6 × 4 = 24

Step 1: Identify what the problem asks

The problem asks for the area of the garden

Step 2: Identify the dimensions

Length = 6 feet, Width = 4 feet

Step 3: Apply the area formula

Area = Length × Width = 6 × 4

Step 4: Calculate and express the answer

Area = 24 square feet

Final answer:

The area of the garden is 24 square feet

Applied rules:

• Area formula: Area = Length × Width

• Multiplication: 6 × 4 = 24

• Area units: Always express in square units

2 Area comparison problem

Exercise 2

Sarah's room is 8 feet long and 5 feet wide. Tom's room is 7 feet long and 6 feet wide. Whose room has the larger area?

Definition:

Area comparison problem: A word problem that requires calculating and comparing areas of different shapes

Sarah's Room

8 × 5 = 40

Tom's Room

7 × 6 = 42

Comparison

42 > 40

Step 1: Calculate Sarah's room area

Area = 8 × 5 = 40 square feet

Step 2: Calculate Tom's room area

Area = 7 × 6 = 42 square feet

Step 3: Compare the areas

42 > 40, so Tom's room is larger

Step 4: State the answer

Tom's room has the larger area

Area Word Problems | Solved Exercises | Mathematics Grade 3

Solution: Exercises 1 to 3

1 Rectangle area word problem

Exercise 1

Sarah's bedroom is 6 feet long and 4 feet wide. What is the area of her bedroom floor?

Definition:

Area word problem: A mathematical problem presented in sentence form that requires finding the area of a shape

Area word problem method:

Read the problem carefully and identify what's being asked
Identify the dimensions (length and width)
Apply the area formula: Area = Length × Width
Calculate and state the answer with units

Length

6 feet

Width

4 feet

Area

6 × 4 = 24

Step 1: Identify what the problem asks

Find the area of Sarah's bedroom floor

Step 2: Identify the dimensions

Length = 6 feet, Width = 4 feet

Step 3: Apply the area formula

Area = Length × Width = 6 × 4

Area = 24 square feet

Final answer:

The area of Sarah's bedroom floor is 24 square feet

Applied rules:

• Area formula: Area = Length × Width

• Multiplication: 6 × 4 = 24

• Area units: Always express in square units

2 Area comparison word problem

Exercise 2

Tom's garden is 5 units long and 3 units wide. Mary's garden is 4 units long and 4 units wide. Whose garden has the larger area?

Definition:

Area comparison: A word problem that requires calculating and comparing areas of different shapes

Tom's Garden

5 × 3 = 15

Mary's Garden

4 × 4 = 16

Comparison

16 > 15

Step 1: Calculate Tom's garden area

Area = 5 × 3 = 15 square units

Step 2: Calculate Mary's garden area

Area = 4 × 4 = 16 square units

Step 3: Compare the areas

16 > 15, so Mary's garden is larger

Tom: 15 sq units | Mary: 16 sq units

Final answer:

Mary's garden has the larger area (16 square units compared to Tom's 15 square units)

Applied rules:

• Area calculation: Calculate each area separately

• Comparison: Compare the calculated areas

• Decision: Determine which is larger

3 Missing dimension word problem

Exercise 3

A rectangular rug has an area of 20 square feet and is 5 feet wide. How long is the rug?

Definition:

Missing dimension: A word problem where area and one dimension are known, requiring the calculation of the missing dimension

Known Area

20 sq ft

Known Width

5 ft

Unknown Length

20 ÷ 5 = 4

Step 1: Write the area formula

Area = Length × Width

Step 2: Substitute known values

20 = Length × 5

Step 3: Solve for unknown length

Length = 20 ÷ 5 = 4 feet

Step 4: Verify the answer

Check: 4 × 5 = 20 ✓

Length = 4 feet, Width = 5 feet, Area = 20 sq ft

Final answer:

The rug is 4 feet long

Applied rules:

• Formula rearrangement: Length = Area ÷ Width

• Division: To find missing dimension

• Verification: Check by multiplying back

Area Word Problems Fundamentals

\text{Area} = \text{Length} \times \text{Width}

Area Formula

Rectangle Area

L × W

Length × Width

Missing Length

Area ÷ Width

Find unknown length

Missing Width

Area ÷ Length

Find unknown width

Key definitions:

Area word problem: A mathematical problem presented in sentence form that requires finding area

Dimension: The measurements of length and width

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

Missing dimension: When area and one dimension are known, find the other dimension

5-step problem-solving method:

Read: Understand what the problem is asking
Identify: Find the important information and dimensions
Plan: Decide which formula to use
Solve: Perform calculations
Check: Verify if the answer makes sense

Tip 1: Underline or circle important numbers in the problem.

Tip 2: Draw a rectangle to visualize the problem.

Tip 3: Always include "square units" in your answer.

Tip 4: Check if your answer is reasonable for the context.

Common errors: Forgetting to multiply, confusing length with width, not including square units.

Memory aid: "Area is Length times Width, always add 'square' to the unit!"

Key area facts:

• Area of rectangle = Length × Width

• Area is always measured in square units

• Missing dimension = Area ÷ Known dimension

• Always verify your answer makes sense

Solution: Exercises 4 to 5

4 Multi-step area problem

Exercise 4

A rectangular playground is 8 meters long and 6 meters wide. If a 2-meter by 2-meter sandbox is placed in the corner, what is the remaining area of the playground?

Definition:

Multi-step area problem: A word problem that requires multiple calculations to find the final answer

Playground Area

8 × 6 = 48

Sandbox Area

2 × 2 = 4

Remaining Area

48 - 4 = 44

Step 1: Calculate playground area

Area = 8 × 6 = 48 square meters

Step 2: Calculate sandbox area

Area = 2 × 2 = 4 square meters

Step 3: Subtract to find remaining area

Remaining area = 48 - 4 = 44 square meters

Solved Exercises on Area Word Problems in Grade 3

Solved Exercises on Area Word Problems in Grade 3

Solved Exercises on Area Word Problems in Grade 3