Area Compound Shapes Worksheet

Understanding Area of Compound Shapes

Compound shapes are made up of two or more simple shapes, such as triangles, rectangles, and circles. To find the area of a compound shape, we need to find the area of each individual shape and then add them together.

What are Compound Shapes?

Compound shapes are shapes that are made up of two or more simple shapes. They can be composed of different types of shapes, such as triangles, quadrilaterals, polygons, and circles. Compound shapes can be found in real-life objects, such as buildings, bridges, and even furniture.

How to Find the Area of Compound Shapes

To find the area of a compound shape, we need to follow these steps:

1. Identify the individual shapes: Break down the compound shape into its individual shapes.
2. Find the area of each shape: Use the formulas for the area of each shape to find their individual areas.
3. Add the areas together: Add the areas of each shape to find the total area of the compound shape.

Example 1: Finding the Area of a Compound Shape Made Up of Rectangles

Problem: Find the area of the compound shape below.

Solution:

1. Identify the individual shapes: We have two rectangles.
2. Find the area of each shape:
   • Area of Rectangle 1 = Length x Width = 6cm x 4cm = 24cm²
   • Area of Rectangle 2 = Length x Width = 8cm x 3cm = 24cm²
3. Add the areas together: Total Area = Area of Rectangle 1 + Area of Rectangle 2 = 24cm² + 24cm² = 48cm²

📝 Note: When finding the area of a compound shape, make sure to add the areas of all the individual shapes.

Example 2: Finding the Area of a Compound Shape Made Up of Triangles

Problem: Find the area of the compound shape below.

Solution:

1. Identify the individual shapes: We have two triangles.
2. Find the area of each shape:
   • Area of Triangle 1 = ¹⁄₂ x Base x Height = ¹⁄₂ x 5cm x 6cm = 15cm²
   • Area of Triangle 2 = ¹⁄₂ x Base x Height = ¹⁄₂ x 8cm x 4cm = 16cm²
3. Add the areas together: Total Area = Area of Triangle 1 + Area of Triangle 2 = 15cm² + 16cm² = 31cm²

📝 Note: When finding the area of a compound shape made up of triangles, make sure to use the formula for the area of a triangle: 1/2 x Base x Height.

Practice Time!

Try finding the area of the following compound shapes:

1. A compound shape made up of two rectangles with dimensions 4cm x 6cm and 8cm x 5cm.
2. A compound shape made up of a triangle with base 6cm and height 8cm, and a rectangle with dimensions 5cm x 4cm.

Remember to identify the individual shapes, find their areas, and add them together to find the total area!

As you practice finding the area of compound shapes, you’ll become more confident in your ability to break down complex shapes into simpler ones and calculate their areas. With time and practice, you’ll master this skill and be able to tackle even the most challenging problems!

Related Terms:

• Perimeter compound shapes worksheets