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 compound shape area problems if you describe the shapes or provide details about them.

But since you've mentioned "Area – Compound Shapes" and there are six labeled diagrams (A to F), I’ll walk you through a general method for solving such problems and then give examples based on typical compound shapes that appear in these types of worksheets.

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🔷 General Strategy for Finding Area of Compound Shapes:

1. Break the shape into simpler shapes (e.g., rectangles, triangles, circles, trapezoids).
2. Find the area of each individual shape using appropriate formulas.
3. Add or subtract areas as needed (if parts are missing or overlapping).
4. Round your final answer to 1 decimal place, as instructed.

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🔷 Common Formulas You Might Need:

- 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 $)
- Trapezoid: $ A = \frac{1}{2} \times (\text{base}_1 + \text{base}_2) \times \text{height} $
- Parallelogram: $ A = \text{base} \times \text{height} $

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Let’s assume typical shapes from such worksheets and solve them one by one:

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🟦 Shape A: Rectangle with a triangle cut out

Suppose it's a rectangle of length 10 cm and width 6 cm, with a right triangle removed at the top (base = 4 cm, height = 3 cm).

- Area of rectangle: $ 10 \times 6 = 60 $ cm²
- Area of triangle: $ \frac{1}{2} \times 4 \times 3 = 6 $ cm²
- Shaded area: $ 60 - 6 = 54.0 $ cm²

✔ Answer: 54.0 cm²

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🟨 Shape B: Right triangle attached to a rectangle

Suppose the rectangle is 8 cm × 5 cm, and the triangle has base 8 cm and height 4 cm.

- Rectangle: $ 8 \times 5 = 40 $
- Triangle: $ \frac{1}{2} \times 8 \times 4 = 16 $
- Total: $ 40 + 16 = 56.0 $ cm²

✔ Answer: 56.0 cm²

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🟩 Shape C: Rectangle with a semicircle on top

Suppose rectangle is 10 cm × 6 cm, and semicircle has diameter 10 cm → radius = 5 cm.

- Rectangle: $ 10 \times 6 = 60 $
- Semicircle: $ \frac{1}{2} \times \pi \times 5^2 = \frac{1}{2} \times 3.14 \times 25 = 39.25 $
- Total: $ 60 + 39.25 = 99.25 \approx 99.3 $ cm²

✔ Answer: 99.3 cm²

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🟪 Shape D: Circle with a sector removed

Suppose full circle radius = 7 cm, and a quarter (90°) is shaded.

- Full area: $ \pi \times 7^2 = 3.14 \times 49 = 153.86 $
- Quarter removed: $ \frac{1}{4} \times 153.86 = 38.47 $
- Shaded area: $ 153.86 - 38.47 = 115.39 \approx 115.4 $ cm²

Wait — but if only the shaded part is the major sector, then it's $ \frac{3}{4} \times 153.86 = 115.395 \approx 115.4 $ cm²

✔ Answer: 115.4 cm²

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🟫 Shape E: L-shaped figure

Split into two rectangles:
- Top: 6 cm × 4 cm = 24
- Bottom: 8 cm × 3 cm = 24
- Total: $ 24 + 24 = 48.0 $ cm²

✔ Answer: 48.0 cm²

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🟥 Shape F: Arrow-like shape (rectangle with triangle on both ends)

Suppose central rectangle: 12 cm × 4 cm = 48
Each triangle: base = 4 cm, height = 4 cm → area = $ \frac{1}{2} \times 4 \times 4 = 8 $
Two triangles: $ 8 \times 2 = 16 $
Total: $ 48 + 16 = 64.0 $ cm²

✔ Answer: 64.0 cm²

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✔ Final Answers (Example):

| Shape | Area (cm²) |
|-------|------------|
| A | 54.0 |
| B | 56.0 |
| C | 99.3 |
| D | 115.4 |
| E | 48.0 |
| F | 64.0 |

> ⚠️ These are example calculations based on common compound shapes. Your actual image may have different dimensions.

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🔍 To Get Accurate Help:

Please describe each shape in words or list the dimensions shown in the image (e.g., lengths, radii, angles). For example:

> "Shape A: A rectangle 12 cm by 8 cm with a triangle cut out from the top. The triangle has base 6 cm and height 4 cm."

Then I can give exact answers matching your image.

Let me know!