# Finding the Area of a Composite Figure

A composite figure is a shape made up of two or more basic geometric shapes, such as rectangles, triangles, and circles. To find the area of a composite figure, we need to break it down into its individual shapes and calculate the area of each shape separately. Then, we can add or subtract the areas as needed to find the total area of the composite figure.

In this tutorial, we will walk you through the process of finding the area of a composite figure step by step.

## Finding the Area of a Composite Figure

### Step 1 – Identify the Individual Shapes

The first step in finding the area of a composite figure is to identify the individual shapes that make up the figure. Look for familiar shapes such as rectangles, squares, triangles, and circles. You may need to divide the composite figure into smaller sections to make it easier to identify these shapes.

For example, let’s say we have a composite figure that consists of a rectangle with a semicircle on top. The individual shapes in this case are the rectangle and the semicircle.

### Step 2 – Calculate the Area of Each Shape

Next, we need to calculate the area of each individual shape. Use the appropriate formula for each shape. Here are some common area formulas:

• Rectangle: Area = length × width
• Triangle: Area = (base × height) / 2
• Circle: Area = π × radius²
• Semicircle: Area = (π × radius²) / 2

Using the example composite figure from Step 1, we will calculate the area of the rectangle and the semicircle. Let’s assume the rectangle has a length of 10 units and a width of 5 units, and the semicircle has a radius of 5 units.

Rectangle area: 10 × 5 = 50 square units Semicircle area: (π × 5²) / 2 = (3.14 × 25) / 2 ≈ 39.25 square units

### Step 3 – Add or Subtract the Areas

Now that we have calculated the area of each individual shape, we need to add or subtract the areas as necessary to find the total area of the composite figure.

For our example, we will add the area of the rectangle and the semicircle, since the semicircle is on top of the rectangle and does not overlap or subtract from the area.

Total area: 50 + 39.25 ≈ 89.25 square units

### Step 4 – Check Your Work

Finally, it’s always a good idea to check your work. Make sure you’ve used the correct formulas and calculated the areas correctly. In our example, we calculated the area of the rectangle and the semicircle correctly and added the areas to find the total area of the composite figure.

## Conclusion

Finding the area of a composite figure requires breaking down the figure into its individual shapes, calculating the area of each shape, and then adding or subtracting the areas as needed. By following these steps and using the appropriate formulas, you can easily find the area of any composite figure. Remember to always check your work to ensure accuracy.

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