Area of Rectangles and Parallelograms Worksheets - 3rd Grade Math

Complete worksheet with exercises on area calculation for rectangles and parallelograms with step-by-step solutions for 3rd grade students.

Area of Rectangles and Parallelograms
Worksheet for 3rd Grade Students

Instructions:

  • For each problem, identify whether it's a rectangle or parallelogram
  • Measure the required dimensions (length and width for rectangles, base and height for parallelograms)
  • Apply the correct area formula
  • Show all your work and write the final answer in square units
  • Check your answer by counting squares when possible
Rectangle: A = l × w
Parallelogram: A = b × h
Area Formulas
Key Concepts:

Rectangle: A 4-sided shape with 4 right angles and opposite sides equal

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

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

Length: The longer side of a rectangle

Width: The shorter side of a rectangle

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

Height: The perpendicular distance from base to top

Problem Solving Steps:
  1. Identify the shape: Determine if it's a rectangle or parallelogram
  2. Measure dimensions: Find the necessary measurements
  3. Select formula: Choose the correct area formula
  4. Substitute values: Plug measurements into the formula
  5. Calculate area: Perform the multiplication
  6. Include units: Add "square units" to your answer
Tip 1: For parallelograms, measure height perpendicular to the base.
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.
Problem Set: Problems 1 to 3
1 Rectangle Area
1
Find the area of a rectangle with length 8 units and width 5 units.
Solution:
Length = 8
Width = 5
Identify the shape: Rectangle
Identify the formula: Area = Length × Width
Substitute values: Area = 8 × 5
Calculate: Area = 40
Include units: 40 square units
Area = Length × Width = 8 × 5 = 40 square units
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Answer:
The area of the rectangle is 40 square units.
Verification:

Counted squares: 40 ✓

Formula: 8 × 5 = 40 ✓

2 Parallelogram Area
2
Find the area of a parallelogram with base 7 units and height 4 units.
Solution:
Base = 7
Height = 4
Identify the shape: Parallelogram
Identify the formula: Area = Base × Height
Substitute values: Area = 7 × 4
Calculate: Area = 28
Include units: 28 square units
Area = Base × Height = 7 × 4 = 28 square units
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Answer:
The area of the parallelogram is 28 square units.
Verification:

Counted squares: 28 ✓

Formula: 7 × 4 = 28 ✓

3 Comparison Problem
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?
Solution:
Length = 6
Width = 3
Base = 6
Height = 3
Rectangle area: Area = Length × Width = 6 × 3 = 18 square units
Parallelogram area: Area = Base × Height = 6 × 3 = 18 square units
Compare: Both shapes have the same area
Rectangle: 6 × 3 = 18
Parallelogram: 6 × 3 = 18
Both have 18 square units
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Answer:
Both shapes have the same area of 18 square units.
Verification:

Rectangle: 6 × 3 = 18 ✓

Parallelogram: 6 × 3 = 18 ✓

Equal dimensions yield equal areas ✓

Problem Set: Problems 4 to 5
4 Real-world Application
4
Sarah 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?
Solution:
Length = 10 ft
Width = 7 ft
Grass Area
Identify the shape: Rectangle
Identify the dimensions: Length = 10 feet, Width = 7 feet
Apply the formula: Area = Length × Width
Substitute values: Area = 10 × 7
Calculate: Area = 70 square feet
Area = Length × Width = 10 × 7 = 70 square feet
<...... Area of Rectangles and Parallelograms Worksheets | 3rd Grade Math | Area and Multiplication

Area of Rectangles and Parallelograms Worksheets - 3rd Grade Math

Complete worksheet with exercises on area calculation for rectangles and parallelograms with step-by-step solutions for 3rd grade students.

Area of Rectangles and Parallelograms
Worksheet for 3rd Grade Students

Instructions:

  • For each problem, identify whether it's a rectangle or parallelogram
  • Measure the required dimensions (length and width for rectangles, base and height for parallelograms)
  • Apply the correct area formula
  • Show all your work and write the final answer in square units
  • Check your answer by counting squares when possible
Rectangle: A = l × w
Parallelogram: A = b × h
Area Formulas
Key Concepts:

Rectangle: A 4-sided shape with 4 right angles and opposite sides equal

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

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

Length: The longer side of a rectangle

Width: The shorter side of a rectangle

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

Height: The perpendicular distance from base to top

Problem Solving Steps:
  1. Identify the shape: Determine if it's a rectangle or parallelogram
  2. Measure dimensions: Find the necessary measurements
  3. Select formula: Choose the correct area formula
  4. Substitute values: Plug measurements into the formula
  5. Calculate area: Perform the multiplication
  6. Include units: Add "square units" to your answer
Tip 1: For parallelograms, measure height perpendicular to the base.
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.
Problem Set: Problems 1 to 3
1 Rectangle Area
1
Find the area of a rectangle with length 8 units and width 5 units.
Solution:
Length = 8
Width = 5
Identify the shape: Rectangle
Identify the formula: Area = Length × Width
Substitute values: Area = 8 × 5
Calculate: Area = 40
Area = 8 × 5 = 40 square units
Answer:
The area of the rectangle is 40 square units.
Verification:

Counting squares: 8 × 5 = 40 squares ✓

Formula: 8 × 5 = 40 ✓

2 Parallelogram Area
2
Find the area of a parallelogram with base 7 units and height 4 units.
Solution:
Base = 7
Height = 4
Identify the shape: Parallelogram
Identify the formula: Area = Base × Height
Substitute values: Area = 7 × 4
Calculate: Area = 28
Area = 7 × 4 = 28 square units
Answer:
The area of the parallelogram is 28 square units.
Verification:

Counting squares: 7 × 4 = 28 squares ✓

Formula: 7 × 4 = 28 ✓

3 Comparison Problem
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?
Solution:
Length = 6
Width = 3
Base = 6
Height = 3
Calculate rectangle area: 6 × 3 = 18 square units
Calculate parallelogram area: 6 × 3 = 18 square units
Compare: Both areas equal 18 square units
Rectangle: 6 × 3 = 18
Parallelogram: 6 × 3 = 18
Both have the same area!
Answer:
Both shapes have the same area of 18 square units.
Verification:

Rectangle: 6 × 3 = 18 ✓

Parallelogram: 6 × 3 = 18 ✓

Same dimensions, same area ✓

Problem Set: Problems 4 to 5
4 Real-world Application
4
Sarah 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?
Solution:
Length = 10 ft
Width = 7 ft
Grass Area
Identify the shape: Rectangle
Identify the formula: Area = Length × Width
Substitute values: Area = 10 × 7
Calculate: Area = 70
Include units: 70 square feet
Area = 10 × 7 = 70 square feet
Answer:
Sarah needs 70 square feet of grass.
Verification:

Formula: 10 × 7 = 70 ✓

Units: Square feet (appropriate for area) ✓

5 Advanced Problem
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?
Solution:
Base = 12 in
Height = 8 in
Banner
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
Area = 12 × 8 = 96 square inches
Cost = 96 × $2 = $192
Answer:
It will cost $192 to create the banner.
Verification:

Area: 12 × 8 = 96 ✓

Cost: 96 × $2 = $192 ✓

Correct formula used: Area = Base × Height ✓

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

Answer: Here are some helpful memory tricks:

  • 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).

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.