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 help you solve problems involving compound shapes (shapes made up of simpler geometric figures like rectangles, triangles, circles, etc.) if you describe them or list the details.

But based on the title and typical structure of such worksheets, here's how to approach finding the area of compound shapes, along with a general explanation:

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🔧 Step-by-Step Method to Find Area of Compound Shapes

1. Break the shape into simpler parts:
- Look for rectangles, triangles, trapezoids, semicircles, etc.
- Draw dashed lines to split the shape if needed.

2. Find the area of each individual part using standard formulas:
- Rectangle: $ A = \text{length} \times \text{width} $
- Triangle: $ A = \frac{1}{2} \times \text{base} \times \text{height} $
- Circle: $ A = \pi r^2 $ (use $ \pi \approx 3.14 $)
- Semicircle: $ A = \frac{1}{2} \pi r^2 $
- Trapezoid: $ A = \frac{1}{2} \times (\text{base}_1 + \text{base}_2) \times \text{height} $

3. Add or subtract areas:
- If the shape is made by combining parts, add their areas.
- If a part is missing (like a rectangle with a hole), subtract the smaller area from the larger one.

4. Round to the nearest tenth as instructed.

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📌 Example Problem (Typical Type)

Let’s say one of the shapes is a rectangle with a semicircle on top:
- Rectangle: 10 cm × 6 cm
- Semicircle: diameter = 10 cm → radius = 5 cm

#### Step 1: Area of rectangle
$$
A_{\text{rect}} = 10 \times 6 = 60 \text{ cm}^2
$$

#### Step 2: Area of semicircle
$$
A_{\text{semi}} = \frac{1}{2} \pi r^2 = \frac{1}{2} \times 3.14 \times 5^2 = \frac{1}{2} \times 3.14 \times 25 = 39.25 \text{ cm}^2
$$

#### Step 3: Total area
$$
A_{\text{total}} = 60 + 39.25 = 99.25 \approx 99.3 \text{ cm}^2
$$

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If you can describe the shapes (e.g., "a rectangle with a triangle on top", or "a square with a semicircle cut out"), or provide the dimensions from the image, I can walk through the exact solution for each one.

Alternatively, if you can type out the dimensions and shapes from the worksheet, I’ll solve all six problems step by step!