Area of Compound Shapes (Composite Shapes) Worksheets - Free Printable

Since I can't view or access uploaded images directly, I can't see the specific compound shapes in your image. However, I can guide you through solving problems involving compound shapes (shapes made up of simpler geometric figures like rectangles, triangles, circles, etc.).

Here’s how to approach such problems:

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🔧 General Steps to Find the Area of Compound Shapes

1. Break the shape into simpler parts:
- Look for rectangles, triangles, circles, trapezoids, or other basic shapes.
- Label each part clearly.

2. Find the area of each individual shape:
- Use appropriate formulas:
- Rectangle: $ A = \text{length} \times \text{width} $
- Triangle: $ A = \frac{1}{2} \times \text{base} \times \text{height} $
- Circle: $ A = \pi r^2 $
- Trapezoid: $ A = \frac{1}{2} \times (\text{base}_1 + \text{base}_2) \times \text{height} $

3. Add or subtract areas as needed:
- If the compound shape is made by adding shapes together → add their areas.
- If a part is cut out (like a hole), subtract that area.

4. Round appropriately:
- Usually to 1 decimal place or nearest whole number, depending on instructions.

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📌 Example Problem (Hypothetical)

Let’s say one of the shapes is a rectangle with a semicircle on top.

- Rectangle: 10 cm × 5 cm → Area = $ 10 \times 5 = 50 \, \text{cm}^2 $
- Semicircle: diameter = 10 cm → radius = 5 cm
- Area of full circle: $ \pi \times 5^2 = 25\pi $
- Area of semicircle: $ \frac{1}{2} \times 25\pi = 12.5\pi \approx 39.27 \, \text{cm}^2 $
- Total area: $ 50 + 39.27 = 89.27 \, \text{cm}^2 $ → Round to 89.3 cm²

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✔ Tips for Your Worksheet

If you describe one of the shapes from the worksheet, I can help solve it step-by-step!

For example:
> "Shape 1 is a rectangle with a semicircle on the right side. The rectangle is 12 cm long and 6 cm wide. The semicircle has a diameter of 6 cm."

Then I can compute it.

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👉 Please describe one of the shapes from the image (or list all six), and I’ll walk you through solving them!