Composite Figures Area Worksheet with Easy Solutions

Understanding Composite Figures

Composite figures are geometric shapes that are made up of two or more simpler shapes, such as triangles, rectangles, and circles. Calculating the area of composite figures can be a bit more challenging than finding the area of simple shapes, but with the right strategies and techniques, it can be done easily.

Types of Composite Figures

There are several types of composite figures, including:

• L-shaped figures: These are figures that consist of two rectangles joined at a right angle.
• T-shaped figures: These are figures that consist of two rectangles joined at a right angle, with one rectangle overlapping the other.
• Rectangular figures with triangles or semicircles: These are figures that consist of a rectangle with a triangle or semicircle attached to one side.
• Circles with triangles or rectangles: These are figures that consist of a circle with a triangle or rectangle attached to one side.

Steps to Calculate the Area of Composite Figures

To calculate the area of a composite figure, follow these steps:

1. Break down the figure into simpler shapes: Identify the individual shapes that make up the composite figure, such as triangles, rectangles, and circles.
2. Calculate the area of each individual shape: Use the formulas for the area of each individual shape to calculate their areas.
3. Add up the areas of the individual shapes: Add up the areas of each individual shape to find the total area of the composite figure.

Example 1: L-Shaped Figure

Find the area of the L-shaped figure below:

Solution:

• Calculate the area of Rectangle 1: Area = Length x Width = 6 cm x 4 cm = 24 cm²
• Calculate the area of Rectangle 2: Area = Length x Width = 3 cm x 4 cm = 12 cm²
• Add up the areas of the two rectangles: Total Area = 24 cm² + 12 cm² = 36 cm²

Example 2: T-Shaped Figure

Find the area of the T-shaped figure below:

Solution:

• Calculate the area of Rectangle 1: Area = Length x Width = 5 cm x 3 cm = 15 cm²
• Calculate the area of Rectangle 2: Area = Length x Width = 2 cm x 3 cm = 6 cm²
• Add up the areas of the two rectangles: Total Area = 15 cm² + 6 cm² = 21 cm²

📝 Note: When calculating the area of a composite figure, make sure to include all the individual shapes that make up the figure.

Common Mistakes to Avoid

When calculating the area of composite figures, there are several common mistakes to avoid:

• Forgetting to include all the individual shapes: Make sure to include all the individual shapes that make up the composite figure.
• Incorrectly calculating the area of individual shapes: Double-check your calculations to ensure that you have correctly calculated the area of each individual shape.
• Not adding up the areas correctly: Make sure to add up the areas of all the individual shapes to find the total area of the composite figure.

Conclusion

Calculating the area of composite figures can be a bit more challenging than finding the area of simple shapes, but with the right strategies and techniques, it can be done easily. By breaking down the figure into simpler shapes, calculating the area of each individual shape, and adding up the areas, you can find the total area of a composite figure.