Area of Rectangle and Parallelogram Worksheets - 3rd Grade Math

Master area calculations with visual learning: rectangles, parallelograms, and step-by-step solutions for 3rd grade students.

Area Formulas and Definitions
Rectangle: \(A = l \times w\)
Rectangle Area Formula
Parallelogram: \(A = b \times h\)
Parallelogram Area Formula
Key Definitions:

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

Parallelogram: A 4-sided shape with opposite sides parallel and equal

Base: The bottom side of a shape used for area calculation

Height: The perpendicular distance from base to top

Length: The longer side of a rectangle

Width: The shorter side of a rectangle

Area Calculation Method:
  1. Identify the shape: Determine if it's a rectangle or parallelogram
  2. Measure dimensions: Find length/width for rectangle or base/height for parallelogram
  3. Apply formula: Use the correct area formula
  4. Multiply: Calculate the area using multiplication
  5. Label: Include square units (sq units, cm², in², etc.)
Tip 1: Always measure the height perpendicular to the base in parallelograms.
Tip 2: Count squares inside the shape to verify your area calculation.
Tip 3: A rectangle is a special type of parallelogram where all angles are 90°.
Tip 4: Remember: Area = Base × Height, not Base × Side in parallelograms.
Common Mistakes: Using side length instead of height for parallelograms, forgetting square units, misidentifying base and height.
Key Memory Aid: "Area equals Base times Height" - works for both rectangles and parallelograms.
Essential Rules:

• Rectangle Area: Length × Width

• Parallelogram Area: Base × Height

• Height is always perpendicular to the base

• Units must be squared in final answer

• Opposite sides are equal in parallelograms

Exercise Solutions: 1 to 3
1 Rectangle Area
Exercise 1
Find the area of a rectangle with length 8 units and width 5 units.
Problem Analysis:

Given: Length = 8 units, Width = 5 units

Formula: Area of rectangle = Length × Width

Length = 8
Width = 5
Formula
\(A = l \times w\)
Substitute
\(A = 8 \times 5\)
Calculate
\(A = 40\)
Step 1: Identify the formula

For rectangles: Area = Length × Width

Step 2: Substitute known values

Area = 8 × 5

Step 3: Perform the multiplication

8 × 5 = 40

Step 4: Add units

Area = 40 square units

Area = 40 square units
Final answer:

The area of the rectangle is 40 square units.

Applied rules:

• Rectangle formula: Area = Length × Width

• Multiplication: 8 × 5 = 40

• Units: Include "square units" in final answer

2 Parallelogram Area
Exercise 2
Find the area of a parallelogram with base 7 units and height 4 units.
Problem Analysis:

Given: Base = 7 units, Height = 4 units

Formula: Area of parallelogram = Base × Height

Base = 7
Height = 4
Formula
\(A = b \times h\)
Substitute
\(A = 7 \times 4\)
Calculate
\(A = 28\)
Step 1: Identify the formula

For parallelograms: Area = Base × Height

Step 2: Substitute known values

Area = 7 × 4

Step 3: Perform the multiplication

7 × 4 = 28

Step 4: Add units

Area = 28 square units

Area = 28 square units
Final answer:

The area of the parallelogram is 28 square units.

Applied rules:

• Parallelogram formula: Area = Base × Height

• Perpendicular height: Height must be perpendicular to base

• Multiplication: 7 × 4 = 28

3 Mixed Shapes
Exercise 3
A rectangle has length 6 units and width 3 units. A parallelogram has base 6 units and height 3 units. Which shape has the larger area?
Problem Analysis:

Rectangle: Length = 6, Width = 3

Parallelogram: Base = 6, Height = 3

Compare: Both shapes have the same dimensions

Length = 6
Width = 3
Base = 6
Height = 3
Rectangle
\(A = 6 \times 3 = 18\)
Parallelogram
\(A = 6 \times 3 = 18\)
Comparison
Both = 18 sq units
Step 1: Calculate rectangle area

Area = 6 × 3 = 18 square units

Step 2: Calculate parallelogram area

Area = 6 × 3 = 18 square units

Step 3: Compare results

Both areas equal 18 square units

Step 4: Draw conclusion

The shapes have equal areas

Both shapes have area = 18 square units
Final answer:

Both shapes have the same area of 18 square units.

Applied rules:

• Rectangle formula: A = l × w

• Parallelogram formula: A = b × h

• Comparison: Equal dimensions yield equal areas

Exercise Solutions: 4 to 5
4 Real-world Application
Exercise 4
Maria wants to plant grass in her rectangular garden that is 10 feet long and 7 feet wide. How many square feet of grass does she need?
Problem Analysis:

Context: Garden is rectangular, need to find area for grass

Given: Length = 10 feet, Width = 7 feet

Formula: Area of rectangle = Length × Width

Length = 10 ft
Width = 7 ft
Grass Area
Formula
\(A = l \times w\)
Substitute
\(A = 10 \times 7\)
Calculate
\(A = 70\)
Step 1: Identify the shape and formula

Garden is rectangular, so Area = Length × Width

Step 2: Identify given measurements

Length = 10 feet, Width = 7 feet

Step 3: Substitute values into formula

Area = 10 × 7

Step 4: Calculate the area

10 × 7 = 70

Step 5: Include appropriate units

Maria needs 70 square feet of grass

Maria needs 70 square feet of grass
Final answer:

Maria needs 70 square feet of grass for her garden.

Applied rules:

• Real-world context: Area represents material needed

• Rectangle formula: A = l × w

• Units: Answer in square feet (ft²)

5 Complex Problem
Exercise 5
A parallelogram-shaped banner has a base of 12 inches and a height of 8 inches. If the banner costs $2 per square inch to make, how much will it cost to create the banner?
Problem Analysis:

Shape: Parallelogram

Given: Base = 12 inches, Height = 8 inches, Cost = $2 per sq inch

Steps: Find area, then multiply by cost per square inch

Base = 12 in
Height = 8 in
Banner
Step 1: Area
\(A = 12 \times 8 = 96\)
Step 2: Cost
\(Cost = 96 \times 2 = 192\)
Final
\$192
Step 1: Calculate the area of the parallelogram

Area = Base × Height = 12 × 8 = 96 square inches

Step 2: Calculate the total cost

Cost = Area × Price per square inch = 96 × $2 = $192

Step 3: Verify the calculation

96 × 2 = 192, so the cost is $192

Step 4: Present the final answer

The banner will cost $192 to create

Banner cost = $192
Final answer:

The banner will cost $192 to create.

Applied rules:

• Parallelogram formula: A = b × h

• Multiplication: Area × Unit cost = Total cost

• Real-world application: Area determines material quantity

Questions & Answers

Question: Why do we multiply length and width to find the area of a rectangle? Can't we just add them?

Answer: Great question! We multiply length and width because area measures how many square units fit inside the rectangle.

Think of it this way: if you have a rectangle that is 3 units long and 4 units wide, imagine filling it with tiny 1-unit squares. You could fit 3 squares along the length, and you can stack 4 rows of these squares along the width. That means you can fit 3 × 4 = 12 squares total inside the rectangle.

If we added them (3 + 4 = 7), we'd get the perimeter (distance around), not the area (space inside). Multiplication tells us how many unit squares cover the entire surface.

Visual example: A 2×3 rectangle has 2 rows of 3 squares each, totaling 2×3=6 squares.

Question: In a parallelogram, why do we use the height instead of the slanted side to calculate area?

Answer: This is a common confusion! The height in a parallelogram is the perpendicular distance from the base to the opposite side, not the length of the slanted side.

Imagine cutting off a triangle from one end of the parallelogram and moving it to the other side. You'd form a rectangle with the same base and height as the original parallelogram. Since the area doesn't change when we rearrange pieces, the parallelogram's area equals the rectangle's area: base × height.

Using the slanted side would give an incorrect result because it doesn't represent how tall the shape really is. The perpendicular height measures the true vertical distance across the shape.

Key: Area = Base × Perpendicular Height, not Base × Slanted Side.

Question: How can I help my child remember the difference between area and perimeter?

Answer: Here are some helpful memory tricks for your child:

  • Perimeter: Think "PERIMETER = PERI-METER (around the meter)" - it's the distance around the edge. Have your child trace their finger around the shape.
  • Area: Think "AREA = A-REALLY-BIG-SQUARE" - it covers the inside space. Have your child color or shade the inside of shapes.
  • Remember: "Perimeter = Pencils around the edge", "Area = Acres of space inside"

Practical activities help too: walk around the room for perimeter, put tiles or blocks inside for area. Use hands-on materials like geoboards or grid paper to visualize the difference.

The key is that perimeter is measured in linear units (cm, inches) while area is measured in square units (cm², in²).