Area of Rectangles Triangles Parallelograms Worksheet - 3rd Grade Math

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

Area of Rectangles, Triangles, and Parallelograms
Worksheet for 3rd Grade Students

Instructions:

  • For each problem, identify the shape (rectangle, triangle, or parallelogram)
  • Measure the required dimensions (base and height for all shapes)
  • Apply the correct area formula for each shape
  • Show all your work and write the final answer in square units
  • Check your answer by counting squares when possible
Rectangle: A = l × w
Triangle: A = ½ × b × h
Parallelogram: A = b × h
Area Formulas
Key Concepts:

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

Triangle: A 3-sided shape with 3 angles

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

Half: One of two equal parts (½)

Problem Solving Steps:
  1. Identify the shape: Determine if it's a rectangle, triangle, 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 and division
  6. Include units: Add "square units" to your answer
Tip 1: For triangles, multiply base × height, then divide by 2.
Tip 2: For parallelograms, measure height perpendicular to the base.
Tip 3: Count squares inside the shape to verify your area calculation.
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 = 8 × 5 = 40 square units
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40
Answer:
The area of the rectangle is 40 square units.
Verification:

Counted squares: 40 ✓

Formula: 8 × 5 = 40 ✓

2 Triangle Area
2
Find the area of a triangle with base 6 units and height 4 units.
Solution:
Base = 6
Height = 4
Identify the shape: Triangle
Identify the formula: Area = ½ × Base × Height
Substitute values: Area = ½ × 6 × 4
Calculate: Area = ½ × 24 = 12
Include units: 12 square units
Area = ½ × 6 × 4 = 12 square units
Area of Rectangles Triangles Parallelograms Worksheet | 3rd Grade Math | Area and Multiplication

Area of Rectangles Triangles Parallelograms Worksheet - 3rd Grade Math

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

Area of Rectangles, Triangles, and Parallelograms
Worksheet for 3rd Grade Students

Instructions:

  • For each problem, identify whether it's a rectangle, triangle, or parallelogram
  • Measure the required dimensions
  • 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
Triangle: A = ½ × b × h
Parallelogram: A = b × h
Area Formulas
Key Concepts:

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

Triangle: A 3-sided shape with 3 angles

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

½: Half of the area of a rectangle with the same base and height

Problem Solving Steps:
  1. Identify the shape: Determine if it's a rectangle, triangle, 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 triangles, remember to multiply by ½ or divide by 2.
Tip 2: For parallelograms, measure height perpendicular to the base.
Tip 3: A triangle is half of a rectangle with the same base and height.
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 Triangle Area
2
Find the area of a triangle with base 6 units and height 4 units.
Solution:
Base = 6
Height = 4
Identify the shape: Triangle
Identify the formula: Area = ½ × Base × Height
Substitute values: Area = ½ × 6 × 4
Calculate: Area = ½ × 24 = 12
Area = ½ × 6 × 4 = 12 square units
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Answer:
The area of the triangle is 12 square units.
Verification:

Counting squares: About 12 squares ✓

Formula: ½ × 6 × 4 = 12 ✓

3 Parallelogram Area
3
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 ✓

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. She also wants to plant flowers in a triangular area with base 6 feet and height 4 feet. How many total square feet of plants does she need?
Solution:
Length = 10 ft
Width = 7 ft
Grass
Base = 6 ft
Height = 4 ft
Flowers
Step 1: Calculate rectangle area (grass)
Area = Length × Width = 10 × 7 = 70 square feet
Step 2: Calculate triangle area (flowers)
Area = ½ × Base × Height = ½ × 6 × 4 = 12 square feet
Step 3: Add both areas
Total = 70 + 12 = 82 square feet
Rectangle: 10 × 7 = 70
Triangle: ½ × 6 × 4 = 12
Total: 70 + 12 = 82
Answer:
Sarah needs 82 square feet of plants in total.
Verification:

Rectangle: 10 × 7 = 70 ✓

Triangle: ½ × 6 × 4 = 12 ✓

Total: 70 + 12 = 82 ✓

5 Advanced Problem
5
A parallelogram-shaped banner has a base of 12 inches and a height of 8 inches. A triangular flag with base 6 inches and height 4 inches will be attached to it. If the banner costs $2 per square inch and the flag costs $1.50 per square inch, what is the total cost to create both shapes?
Solution:
Base = 12 in
Height = 8 in
Banner
Base = 6 in
Height = 4 in
Flag
Step 1: Calculate parallelogram area
Area = Base × Height = 12 × 8 = 96 square inches
Step 2: Calculate triangle area
Area = ½ × Base × Height = ½ × 6 × 4 = 12 square inches
Step 3: Calculate banner cost
Cost = 96 × $2 = $192
Step 4: Calculate flag cost
Cost = 12 × $1.50 = $18
Step 5: Calculate total cost
Total = $192 + $18 = $210
Parallelogram: 12 × 8 = 96 sq in
Triangle: ½ × 6 × 4 = 12 sq in
Banner: 96 × $2 = $192
Flag: 12 × $1.50 = $18
Total: $192 + $18 = $210
Answer:
The total cost to create both shapes is $210.
Verification:

Parallelogram: 12 × 8 = 96 ✓

Triangle: ½ × 6 × 4 = 12 ✓

Banner cost: 96 × $2 = $192 ✓

Flag cost: 12 × $1.50 = $18 ✓

Total: $192 + $18 = $210 ✓

Questions & Answers

Question: Why do we multiply length and width to find the area of a rectangle? And why do we multiply by ½ for triangles?

Answer: Great questions! 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.

For triangles, we multiply by ½ because a triangle is exactly half of a rectangle with the same base and height. If you draw a rectangle and cut it diagonally, you get two identical triangles. So each triangle has half the area of the rectangle.

Visual example: A 2×3 rectangle has 2×3=6 squares. A triangle with base 2 and height 3 has ½×2×3=3 squares.

Question: How can I help my child remember which formula to use for each shape?

Answer: Here are some helpful memory tricks:

  • Rectangle: "Rectangle = Length × Width" - think "Right angles make rectangles"
  • Triangle: "Triangle = ½ × Base × Height" - think "Three sides, half the area"
  • Parallelogram: "Parallelogram = Base × Height" - think "Parallel sides mean same formula as rectangle"
  • For triangles specifically: "Triangle is half of a rectangle with same base and height"

Practice with physical shapes cut out of paper - fold rectangles to see triangles, or cut parallelograms to rearrange into rectangles. Hands-on activities help cement the formulas in memory.

Always emphasize that height is perpendicular to the base in all shapes!

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.