Solved Exercises on Area of Composite Shapes in Grade 4

Master area of composite shapes: rectangles, squares, triangles combined with these 3 detailed exercises.

Solution: Exercises 1 to 3
1 Rectangle and Square
Exercise 1
Find the area of this composite shape:
A rectangle (6 cm × 4 cm) attached to a square (3 cm × 3 cm)
Definition:

Composite shape: A shape made up of two or more basic geometric shapes

Method:
  1. Identify the individual shapes in the composite figure
  2. Calculate the area of each individual shape
  3. Add the areas together to get the total area
Step 1: Identify the shapes

This composite shape has 2 parts: a rectangle and a square

Step 2: Calculate area of rectangle

Area of rectangle = length × width = 6 cm × 4 cm = 24 cm²

Step 3: Calculate area of square

Area of square = side × side = 3 cm × 3 cm = 9 cm²

Step 4: Add the areas

Total area = 24 cm² + 9 cm² = 33 cm²

Total area = 33 cm²
Final answer:

The area of the composite shape is 33 cm²

Applied rules:

• Area of rectangle: length × width

• Area of square: side × side

• Composite area: Sum of individual areas

2 Rectangle and Triangle
Exercise 2
Find the area of this composite shape:
A rectangle (8 cm × 5 cm) with a triangle (base 8 cm, height 3 cm) on top
Definition:

Triangle area: (base × height) ÷ 2

Step 1: Identify the shapes

This composite shape has 2 parts: a rectangle and a triangle

Step 2: Calculate area of rectangle

Area of rectangle = length × width = 8 cm × 5 cm = 40 cm²

Step 3: Calculate area of triangle

Area of triangle = (base × height) ÷ 2 = (8 cm × 3 cm) ÷ 2 = 24 ÷ 2 = 12 cm²

Step 4: Add the areas

Total area = 40 cm² + 12 cm² = 52 cm²

Total area = 52 cm²
Final answer:

The area of the composite shape is 52 cm²

Applied rules:

• Area of rectangle: length × width

• Area of triangle: (base × height) ÷ 2

• Composite area: Sum of individual areas

3 Two Rectangles
Exercise 3
Find the area of this composite shape:
A large rectangle (10 cm × 6 cm) with a smaller rectangle (4 cm × 3 cm) cut out
Definition:

Subtracted area: When one shape is cut out from another, subtract the cut-out area from the main area

Step 1: Identify the shapes

This composite shape has: a large rectangle with a smaller rectangle cut out

Step 2: Calculate area of large rectangle

Area of large rectangle = length × width = 10 cm × 6 cm = 60 cm²

Step 3: Calculate area of small rectangle

Area of small rectangle = length × width = 4 cm × 3 cm = 12 cm²

Step 4: Subtract the cut-out area

Total area = 60 cm² - 12 cm² = 48 cm²

Total area = 48 cm²
Final answer:

The area of the composite shape is 48 cm²

Applied rules:

• Area of rectangle: length × width

• Subtracted area: Main area - cut-out area

• Composite area: Sum or difference of individual areas

Area Formulas and Methods
Area = Length × Width
Rectangle Area
Area = Side × Side
Square Area
Area = (Base × Height) ÷ 2
Triangle Area
Key definitions:

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

Composite shape: A shape made up of two or more basic geometric shapes

Square unit: A unit of measurement for area (cm², m², in², ft²)

Complete methodology:
  1. Break down: Separate the composite shape into basic shapes
  2. Measure: Find the dimensions needed for each basic shape
  3. Calculate: Find the area of each basic shape using the correct formula
  4. Combine: Add areas together OR subtract cut-out areas
  5. Label: Don't forget to include the correct square units
Tip 1: Always identify the basic shapes first before calculating.
Tip 2: When part of a shape is cut out, subtract that area from the main shape.
Tip 3: Count squares if the shape is drawn on grid paper.
Tip 4: Remember to label your final answer with square units (cm², m², etc.).
Common mistakes: Forgetting to use square units, miscounting dimensions, adding instead of subtracting cut-out areas.
Success strategies: Break complex shapes into simple ones, double-check measurements, verify your arithmetic.
Essential formulas:

• Rectangle area: length × width

• Square area: side × side

• Triangle area: (base × height) ÷ 2

• Composite area: sum or difference of parts

Visual Guide to Composite Shapes
Basic Shapes
🔷
Square

All sides equal

Area = side × side

Rectangle

Opposite sides equal

Area = length × width

Triangle

Three-sided shape

Area = (base × height) ÷ 2

Composite Examples
🧩
Addition Example

Rectangle + Square

Areas are added

Subtraction Example

Main shape - Cut-out

Areas are subtracted

Problem-Solving Steps
📋
How to Solve
1
Identify Shapes
2
Find Dimensions
3
Calculate Areas
4
Combine Areas
Grid Method

Count the squares to find area

Practice Makes Perfect!
Q&A: Common Questions

Question: How do I know whether to add or subtract areas when finding the area of a composite shape?

Answer: Great question! It depends on how the shapes are arranged:

  • If shapes are joined together (side by side or stacked), you add their areas
  • If one shape is inside another (like a hole cut out), you subtract the inner shape's area from the outer shape's area

Think of it like this: when shapes are combined, you're covering more space (so add). When part of a shape is removed, you have less space (so subtract).

Example: If you have a big rectangle with a smaller rectangle cut out of it, you'd calculate: (Big rectangle area) - (Small rectangle area) = Total area.

Question: My child is struggling to break down complex shapes. How can I help them see the simpler shapes within a composite figure?

Answer: This is a common challenge! Try these strategies:

  • Outline the shapes: Have your child use different colored pencils to trace each basic shape
  • Look for straight lines: Most composite shapes are divided by straight lines forming rectangles, squares, or triangles
  • Start simple: Begin with shapes that have clear divisions, then progress to more complex figures
  • Use grid paper: This helps visualize how shapes fit together

Encourage your child to look for familiar shapes like rectangles, squares, and triangles. Often, drawing dashed lines to separate the shapes makes it easier to see the individual parts.

Question: Why do I need to learn about composite shapes? When will I ever use this in real life?

Answer: Composite shapes are everywhere in real life! Here are some examples:

  • Home design: Calculating paint needed for walls with windows and doors
  • Gardening: Finding area for sod or mulch in oddly shaped yards
  • Crafting: Determining fabric needed for quilt patterns
  • Construction: Measuring materials for roofs, floors, and walls

Understanding composite shapes helps you solve practical problems like determining how much carpet is needed for a room with closets, or how much tile to buy for a bathroom with a shower niche. These skills are valuable for many careers and everyday situations!