Solved Exercises on Area of Rectangles in Grade 3

Master area of rectangles: length × width formula, counting unit squares, and solving area word problems through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Basic rectangle area
Exercise 1
Find the area of a rectangle that is 3 units long and 4 units wide.
Definition:

Rectangle area: The area of a rectangle is found by multiplying its length by its width

Area formula method:
  1. Identify the length and width of the rectangle
  2. Apply the formula: Area = Length × Width
  3. Perform the multiplication
  4. State the answer in square units
Length
3 units
Width
4 units
Area
3 × 4 = 12
Step 1: Identify dimensions

Length = 3 units, Width = 4 units

Step 2: Apply the formula

Area = Length × Width

Step 3: Calculate

Area = 3 × 4 = 12 square units

Area = 12 square units
Final answer:

The area of the rectangle is 12 square units

Applied rules:

• Rectangle area: Area = Length × Width

• Multiplication: 3 × 4 = 12

• Area units: Always express in square units

2 Square area
Exercise 2
Find the area of a square that is 5 units on each side.
Definition:

Square area: A special rectangle where length and width are equal

Side Length
5 units
Length
5 units
Width
5 units
Area
5 × 5 = 25
Step 1: Identify the side length

All sides = 5 units

Step 2: Apply rectangle area formula

Area = Length × Width = 5 × 5

Step 3: Calculate

Area = 25 square units

Area = 25 square units
Final answer:

The area of the square is 25 square units

Applied rules:

• Square area: Area = Side × Side

• Multiplication: 5 × 5 = 25

• Area units: Always express in square units

3 Area with counting method
Exercise 3
Verify the area of a 2×6 rectangle by counting unit squares.
Definition:

Counting method: Finding area by counting the number of unit squares inside a shape

Dimensions
2 × 6
Formula
2 × 6 = 12
Counting
12 squares
Step 1: Apply formula

Area = 2 × 6 = 12 square units

Step 2: Count unit squares

Count each square: 1, 2, 3, ..., 12

Step 3: Verify both methods match

Formula: 12, Counting: 12 ✓

Step 4: State the result

Area = 12 square units

Area = 12 square units
Final answer:

The area of the rectangle is 12 square units

Applied rules:

• Formula method: Length × Width

• Counting method: Count each unit square

• Verification: Both methods should yield the same result

Rectangle Area Fundamentals
\text{Area} = \text{Length} \times \text{Width}
Rectangle Area Formula
Rectangle
L × W
Length × Width
Square
S × S
Side × Side
Unit Square
1 × 1 = 1
Basic area unit
Key definitions:

Rectangle: A four-sided shape with four right angles

Length: The longer side of a rectangle

Width: The shorter side of a rectangle

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

3-step area calculation method:
  1. Identify: Find the length and width of the rectangle
  2. Multiply: Apply the formula: Area = Length × Width
  3. Verify: Check if the answer makes sense
Tip 1: Always include "square units" in your answer.
Tip 2: Draw a grid to visualize unit squares if needed.
Tip 3: Remember: Area = Length × Width for all rectangles.
Tip 4: A square is a special rectangle where length = width.
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 rectangle facts:

• Area of rectangle = Length × Width

• Area of square = Side × Side

• Area is always measured in square units

• Counting unit squares verifies the formula

Solution: Exercises 4 to 5
4 Missing dimension problem
Exercise 4
A rectangle has an area of 18 square units and a width of 3 units. What is its length?
Definition:

Missing dimension: Finding one dimension when area and the other dimension are known

Known Area
18 sq units
Known Width
3 units
Unknown Length
18 ÷ 3 = 6
Step 1: Write the area formula

Area = Length × Width

Step 2: Substitute known values

18 = Length × 3

Step 3: Solve for unknown length

Length = 18 ÷ 3 = 6 units

Step 4: Verify the answer

Check: 6 × 3 = 18 ✓

Length = 6 units, Width = 3 units, Area = 18 sq units
Final answer:

The length of the rectangle is 6 units

Applied rules:

• Reverse operation: Division to find missing dimension

• Formula rearrangement: Length = Area ÷ Width

• Verification: Check by substituting back into formula

5 Area comparison word problem
Exercise 5
Sarah has a rectangular garden that is 4 units long and 5 units wide. Tom has a rectangular garden that is 3 units long and 7 units wide. Whose garden has the larger area?
Definition:

Area word problem: A real-world problem that requires calculating and comparing areas using the rectangle area formula

Sarah's Garden
4 × 5 = 20
Tom's Garden
3 × 7 = 21
Comparison
21 > 20
Step 1: Calculate Sarah's garden area

Area = 4 × 5 = 20 square units

Step 2: Calculate Tom's garden area

Area = 3 × 7 = 21 square units

Step 3: Compare the areas

21 > 20, so Tom's garden is larger

Step 4: State the answer

Tom's garden has the larger area

Sarah: 20 sq units | Tom: 21 sq units
Final answer:

Tom's garden has the larger area (21 square units compared to Sarah's 20 square units)

Applied rules:

• Rectangle area: Length × Width

• Comparison: Compare calculated areas

• Word problems: Extract dimensions from text

Complete Rectangle Area Guide
\text{Area} = \text{Length} \times \text{Width}
Essential Rectangle Formula
Key definitions:

Area: The amount of space inside a 2D shape, measured in square units

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

Length: The longer dimension of a rectangle

Width: The shorter dimension of a rectangle

Advanced rectangle techniques:
  1. Formula method: Area = Length × Width (most efficient)
  2. Counting method: Count unit squares to verify formula
  3. Reverse calculation: Find missing dimension when area is known
  4. Comparison: Compare areas of different rectangles
Tip 1: Practice with physical manipulatives to visualize area.
Tip 2: Always include "square units" in your final answer.
Tip 3: For missing dimensions, use division: Length = Area ÷ Width.
Tip 4: Draw a sketch to visualize the rectangle before calculating.
Common errors: Forgetting to multiply, confusing length with width, not using proper units.
Success strategies: Regular practice, visual aids, real-world applications.
Essential rectangle facts:

• Area measures the inside space of a rectangle

• Area is always expressed in square units

• Rectangle area = Length × Width

• Square area = Side × Side

Rectangle Area Relationships
Length × Width Patterns
Understanding how different length and width combinations affect area:
Same area, different dimensions

Rectangle Dimensions and Areas:

  • 1 × 12: Area = 12 square units
  • 2 × 6: Area = 12 square units
  • 3 × 4: Area = 12 square units
  • 4 × 3: Area = 12 square units
  • All have same area: Different shapes, same space

Questions & Answers

Question: How do I know which is length and which is width in a rectangle?

Answer: Traditionally:

  • Length: The longer side of the rectangle
  • Width: The shorter side of the rectangle

However, since multiplication is commutative (3 × 4 = 4 × 3), it doesn't matter which dimension you call length or width as long as you multiply both dimensions together.

Some people remember: "Length is how long it is, Width is how wide it is!"

Question: What if the rectangle has decimal numbers like 3.5 units long and 2.5 units wide?

Answer: The formula still works the same way:

  • Area = Length × Width
  • Example: 3.5 × 2.5 = 8.75 square units

For now, focus on whole number dimensions in grade 3. Decimal calculations come in later grades.

The important thing is to understand that the formula applies to all rectangles!

Question: Can a rectangle have the same area as a square? How do I compare them?

Answer: Yes! Rectangles and squares can have the same area:

  • Square: 4 × 4 = 16 square units
  • Rectangle: 2 × 8 = 16 square units
  • Both have same area: 16 square units

To compare, just calculate each area and compare the numbers.

The shape might be different, but the space inside can be the same!