Solved Exercises on Area of a Rectangle in Grade 3

Master area of rectangles: calculating area, finding missing dimensions, comparing areas, and solving word problems through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Basic area calculation
Exercise 1
Find the area of a rectangle with length 8 cm and width 5 cm.
Definition:

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

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

Area calculation method:
  1. Identify the length and width of the rectangle
  2. Multiply length by width
  3. Add the square unit to the answer
Given
Length = 8 cm, Width = 5 cm
Formula
Area = l × w
Answer
40 cm²
Step 1: Identify the measurements

Length = 8 cm, Width = 5 cm

Step 2: Apply the area formula

Area = length × width = 8 × 5

Step 3: Calculate the result

8 × 5 = 40

Step 4: Add the unit

Area = 40 square centimeters or 40 cm²

Area = 40 cm²
Final answer:

The area of the rectangle is 40 cm²

Applied rules:

• Area Formula: Area = length × width

• Units: Always include square units (cm², m², etc.)

• Multiplication: Multiply the numerical values correctly

2 Finding missing dimension
Exercise 2
A rectangle has an area of 24 cm² and a width of 4 cm. What is its length?
Definition:

Missing dimension: When you know the area and one dimension, you can find the other using division

Given
Area = 24 cm², Width = 4 cm
Formula
Length = Area ÷ Width
Answer
6 cm
Step 1: Write down what you know

Area = 24 cm², Width = 4 cm, Length = ?

Step 2: Use the inverse operation

If Area = length × width, then Length = Area ÷ width

Step 3: Substitute known values

Length = 24 ÷ 4

Step 4: Calculate

24 ÷ 4 = 6

Step 5: Add the unit

Length = 6 cm

Length = 6 cm
Final answer:

The length of the rectangle is 6 cm

Applied rules:

• Inverse Operations: Division is the inverse of multiplication

• Area Formula Rearrangement: Length = Area ÷ Width

• Verification: Check by multiplying: 6 × 4 = 24 ✓

3 Word problem application
Exercise 3
Sarah wants to carpet her rectangular bedroom. The room is 6 feet long and 4 feet wide. How many square feet of carpet does she need?
Definition:

Word problem: Real-life situation requiring mathematical solution using area calculation

Given
Length = 6 ft, Width = 4 ft
Formula
Area = l × w
Result
24 ft²
Step 1: Identify the key information

Rectangular room: length = 6 feet, width = 4 feet

Step 2: Determine what is being asked

How much carpet is needed? This means find the area.

Step 3: Apply the area formula

Area = length × width = 6 × 4

Step 4: Calculate the area

6 × 4 = 24

Step 5: Include the proper unit

Since measurements are in feet, the area is 24 square feet

Sarah needs 24 ft² of carpet
Final answer:

Sarah needs 24 square feet of carpet for her bedroom

Applied rules:

• Problem Solving: Identify given information and what is asked

• Real-world Application: Area represents covering a surface

• Unit Consistency: Use same units for length and width

Rules and methods, laws,...
Area = length × width
Area of a Rectangle
Formula
A = l × w
Area equals length times width
Finding Length
l = A ÷ w
Length equals area divided by width
Finding Width
w = A ÷ l
Width equals area divided by length
Key definitions:

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

Length: The longer side of a rectangle

Width: The shorter side of a rectangle

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

Complete methodology:
  1. Identify the rectangle: Recognize the shape has four right angles
  2. Find measurements: Locate length and width values
  3. Apply formula: Use Area = length × width
  4. Calculate: Perform the multiplication
  5. Include units: Add square units (cm², m², ft², etc.)
Tip 1: Count the number of square units inside a rectangle to understand area visually.
Tip 2: Always multiply length by width, regardless of which measurement is larger.
Tip 3: To find a missing dimension, divide the area by the known dimension.
Tip 4: Remember that area is always expressed in square units.
Common errors: Forgetting to include square units, mixing up length and width, adding instead of multiplying.
Key facts: A square is a special rectangle where length equals width.
Formulas to know by heart:

• Area of rectangle: A = l × w

• Finding length: l = A ÷ w

• Finding width: w = A ÷ l

• Area of square: A = s × s = s²

Exercise with Visualization: Comparing Areas
Exercise 6: Area Comparison
Compare the areas of different rectangles:
Rectangle A: 5 cm × 3 cm
Rectangle B: 4 cm × 4 cm
Rectangle C: 6 cm × 2 cm

Analysis: The chart shows the areas of different rectangles calculated using the area formula.

  • Rectangle A: 5 × 3 = 15 cm²
  • Rectangle B: 4 × 4 = 16 cm² (Square)
  • Rectangle C: 6 × 2 = 12 cm²

Questions & Answers

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

Answer: Great question! Think of area as counting the number of square units that fit inside a rectangle.

  • If you have a rectangle that is 3 units long and 4 units wide, imagine filling it with 1×1 squares.
  • You can fit 3 squares along the length and 4 squares along the width.
  • Total squares = 3 rows × 4 columns = 12 squares

If you added (3 + 4 = 7), you'd only count the edges, not the space inside!

Multiplication tells us how many squares fill the entire rectangle: length × width = total squares.

Example: A 5 cm × 3 cm rectangle has 5 groups of 3 square units = 5 × 3 = 15 cm².

Question: How do I know which side is length and which is width? Sometimes they look the same.

Answer: You're right that sometimes it's hard to tell! Here's the important thing to remember:

  • Traditionally, the longer side is called the length, and the shorter side is called the width.
  • However, for the area formula, it doesn't matter which is which because multiplication is commutative (a × b = b × a).
  • So 5 × 3 = 15 and 3 × 5 = 15 - same result!

In word problems, the problem usually tells you both dimensions.

Example: If a rectangle is 4 cm by 7 cm, it doesn't matter if you call 7 the length or 4 the length - area = 4 × 7 = 28 cm².

Just make sure you multiply BOTH dimensions together!

Question: What happens if I forget to write the square units in my answer?

Answer: Including square units is extremely important! Here's why:

  • Area vs Length: Without square units, people might think you're giving a length measurement instead of an area.
  • Context: Units tell us what type of measurement you found (square centimeters vs centimeters).
  • Accuracy: In math and real life, units are part of the answer.

Example: If you say "the area is 24" instead of "the area is 24 cm²", someone might think you mean the length is 24 cm!

Always include square units: cm², m², ft², in², etc.

A helpful memory trick: "Area ends in SQUARE units!"