Solved Exercises on Area Measurement in Grade 3

Master area measurement: counting unit squares, calculating area of rectangles, and comparing areas through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Counting Unit Squares
Exercise 1
Find the area of the shape below by counting unit squares:
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Definition:

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

Unit Square: A square with sides of length 1 unit. Area = 1 square unit.

Counting Method:
  1. Count each complete unit square inside the shape
  2. Add partial squares if needed (2 half-squares = 1 full square)
  3. Total count = area in square units
Shape Dimensions
Length = 5 units
Width = 3 units
Total Count
15 squares
Step 1: Count squares in first row

Row 1: 1, 2, 3, 4, 5 squares = 5 squares

Step 2: Count squares in second row

Row 2: 6, 7, 8, 9, 10 squares = 5 squares

Step 3: Count squares in third row

Row 3: 11, 12, 13, 14, 15 squares = 5 squares

Step 4: Add all rows together

5 + 5 + 5 = 15 squares total

Area = 15 square units
Final answer:

The area of the rectangle is 15 square units.

Applied rules:

• Counting: Each unit square represents 1 square unit of area

• Consistency: Count systematically to avoid missing or double-counting squares

• Verification: Use length × width to verify: 5 × 3 = 15 ✓

2 Area of Rectangle
Exercise 2
Find the area of a rectangle with length 6 units and width 4 units.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Definition:

Rectangle Area Formula: Area = Length × Width

Given
Length = 6
Width = 4
Formula
Area = L × W
Result
24 sq units
Step 1: Identify dimensions

Length = 6 units, Width = 4 units

Step 2: Apply the formula

Area = Length × Width = 6 × 4

Step 3: Calculate the product

6 × 4 = 24

Step 4: State the answer with units

Area = 24 square units

Area = 24 square units
Final answer:

The area of the rectangle is 24 square units.

Applied rules:

• Multiplication: Area of rectangle = length × width

• Units: Always include "square units" in your answer

• Verification: Count squares to confirm: 6 columns × 4 rows = 24 squares ✓

3 Comparing Areas
Exercise 3
Shape A: 4 units long, 3 units wide
Shape B: 5 units long, 2 units wide
Which shape has a larger area?
Definition:

Area Comparison: Calculate each area separately, then compare the results.

Shape A
4 × 3 = 12
Shape B
5 × 2 = 10
Comparison
12 > 10
Step 1: Calculate area of Shape A

Area A = Length × Width = 4 × 3 = 12 square units

Step 2: Calculate area of Shape B

Area B = Length × Width = 5 × 2 = 10 square units

Step 3: Compare the areas

12 square units > 10 square units

Step 4: State the conclusion

Shape A has a larger area than Shape B

Shape A (12 sq units) > Shape B (10 sq units)
Final answer:

Shape A has a larger area (12 square units) than Shape B (10 square units).

Applied rules:

• Calculation: Find each area separately using the formula

• Comparison: Compare numerical values to determine which is larger

• Explanation: Always state which shape has the larger area

Rules and methods, laws,...
Area = Length × Width
Rectangle Area Formula
Rule 1
Area = Length × Width
For Rectangles
Rule 2
Count Unit Squares
For Any Shape
Rule 3
Compare Numerically
For Area Comparison
Key definitions:

Area: The amount of space inside a 2D shape

Unit Square: A square with 1 unit length on each side

Dimensions: Length and width of a rectangle

Complete methodology:
  1. Identify the shape: Determine if it's a rectangle or irregular shape
  2. Choose the method: Use formula for rectangles, counting for irregular shapes
  3. Apply the method: Calculate using the chosen technique
  4. State the answer: Include proper units (square units)
Tip 1: Remember to multiply length by width to find area of rectangles.
Tip 2: Count squares systematically row by row to avoid mistakes.
Tip 3: Always write "square units" in your final answer.
Tip 4: Use multiplication facts to quickly calculate area.
Common errors: Forgetting units, miscounting squares, confusing area with perimeter.
Exam preparation: Practice multiplication tables, visualize area, compare shapes.
Formulas to know by heart:

• Area of rectangle = Length × Width

• Area of square = Side × Side = Side²

• Area of any shape = Count unit squares inside

• Units: Always express area in square units

Solution: Exercises 4 to 5
4 Irregular Shape Area
Exercise 4
Find the area of the irregular shape below:
1
2
3
4
5
6
7
8
9
10
11
12
Definition:

Irregular Shape: A shape that doesn't have equal sides or angles. Area found by counting unit squares.

Shape
Irregular
Method
Counting
Result
12 sq units
Step 1: Count squares in top row

Row 1: 3 filled squares (1, 2, 3) = 3 squares

Step 2: Count squares in middle row

Row 2: 4 filled squares (4, 5, 6, 7) = 4 squares

Step 3: Count squares in bottom row

Row 3: 5 filled squares (8, 9, 10, 11, 12) = 5 squares

Step 4: Add all squares

Total = 3 + 4 + 5 = 12 squares

Area = 12 square units
Final answer:

The area of the irregular shape is 12 square units.

Applied rules:

• Counting: For irregular shapes, count each unit square

• Organization: Count systematically row by row

• Accuracy: Only count filled squares, ignore empty spaces

5 Finding Missing Dimension
Exercise 5
A rectangle has an area of 20 square units and a width of 4 units. Find the length.
Definition:

Missing Dimension: When area and one dimension are known, use division to find the other dimension.

Given
Area = 20
Width = 4
Formula
Length = Area ÷ Width
Result
Length = 5
Step 1: Write the area formula

Area = Length × Width

Step 2: Substitute known values

20 = Length × 4

Step 3: Solve for unknown dimension

Length = 20 ÷ 4 = 5

Step 4: Verify the answer

Area = Length × Width = 5 × 4 = 20 ✓

Length = 5 units
Final answer:

The length of the rectangle is 5 units.

Applied rules:

• Rearrangement: If Area = Length × Width, then Length = Area ÷ Width

• Division: Use division to find missing dimension

• Verification: Always check by multiplying to get original area

Area Measurement Fundamentals and Properties
Area = Length × Width
Area Calculation
Key definitions:

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

Unit Square: A square with sides of 1 unit length, used as a standard for measuring area

Dimensions: The measurements that define the size of a shape (length, width)

Complete methodology:
  1. Identify the shape: Recognize whether it's regular (rectangle, square) or irregular
  2. Choose the method: Use formula for regular shapes, counting for irregular shapes
  3. Apply the method: Perform calculations systematically
  4. Verify the result: Check by counting or using alternative method
Tip 1: Remember that area measures surface, not distance around (perimeter).
Tip 2: For rectangles, you can count rows and multiply by number of columns.
Tip 3: When finding missing dimensions, use inverse operations (division).
Tip 4: Always check your work by using a different method to verify.
Properties of Area: Area is additive (areas of parts sum to whole area), invariant under rotation, and proportional to scale factor squared.
Real-world Applications: Measuring rooms, gardens, fields, and surfaces for coverage calculations.
Essential formulas and rules:

• Area of rectangle = Length × Width

• Area of square = Side × Side = Side²

• Area of any shape = Count unit squares inside

• Units: Always express area in square units (sq units, cm², m², etc.)

• Missing dimension: Length = Area ÷ Width, Width = Area ÷ Length

Area Visualization: Different Shapes and Sizes
Exercise 6: Comparing Areas Visually
Consider the following rectangles:
Rectangle A: 3 units × 4 units
Rectangle B: 2 units × 6 units
Rectangle C: 5 units × 2 units

Analysis: All rectangles have the same area of 12 square units, showing that different dimensions can result in the same area.

  • Rectangle A: 3 × 4 = 12 square units
  • Rectangle B: 2 × 6 = 12 square units
  • Rectangle C: 5 × 2 = 10 square units

Questions & Answers

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

Answer: Great question! Think of area as covering a surface with unit squares:

  • If you have a rectangle that is 3 units long and 4 units wide, imagine placing unit squares to cover it completely.
  • You can fit 3 squares along the length and 4 squares along the width.
  • This creates 4 rows of 3 squares each, which is 4 × 3 = 12 squares total.
  • If you added (3 + 4 = 7), you'd only get 7, which is much less than the 12 squares that actually fit!

Multiplication tells us how many squares fit in total, while addition would just tell us the combined lengths of two sides.

Question: When I'm counting squares for area, I sometimes lose track. How can I make sure I count correctly?

Answer: Here are some helpful strategies for accurate counting:

  • Count systematically: Go row by row from left to right, top to bottom
  • Mark as you count: Put a small dot or checkmark in each square as you count it
  • Group counting: Count by 2s, 5s, or 10s if the squares are arranged in groups
  • Double-check: Count once going across, then count again going down to verify

For rectangles, you can also multiply the number of squares in one row by the number of rows, which is faster and more accurate!

Question: What's the difference between area and perimeter? They seem similar.

Answer: Area and perimeter are different measurements:

  • Area: Measures the space inside a shape. It's like filling the shape with unit squares. Units: square units (sq units, cm², m²)
  • Perimeter: Measures the distance around the outside of a shape. It's like walking along the edges. Units: linear units (cm, m, inches)

Example: A 3×4 rectangle has:

  • Area = 3 × 4 = 12 square units (space inside)
  • Perimeter = 3 + 4 + 3 + 4 = 14 units (distance around)

Think of area as carpeting a room and perimeter as putting trim around the walls!