SOLUTION: Area compund shapes 2 - Studypool - Free Printable

It looks like you've uploaded a worksheet titled "Area - Compound Shapes", which asks students to find the area of various compound (composite) shapes. The image is blurry, so I can't read all the exact measurements or labels clearly, but based on the layout and typical problems of this type, I’ll walk through how to solve each kind of compound shape step by step.

Since the image is not clear enough for me to extract precise dimensions, I will explain the general method for solving such problems and provide an example solution for one of the shapes assuming common values.

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🔷 General Strategy for Finding Area of Compound Shapes:

1. Break the shape into simpler geometric parts (e.g., rectangles, triangles, circles, trapezoids).
2. Find the area of each individual part using standard formulas.
3. Add or subtract areas as needed (if some parts are cut out).
4. Round your final answer to 2 decimal places if required.

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📐 Common Area 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} $

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✔ Example: Let's Solve Shape #1 (Top Left)

Assume the shape is:
- A rectangle with height 5 cm and width 10 cm
- A triangle on top with base 4 cm and height 3 cm

#### Step 1: Area of Rectangle
$$
A_{\text{rect}} = 10 \times 5 = 50 \text{ cm}^2
$$

#### Step 2: Area of Triangle
$$
A_{\text{tri}} = \frac{1}{2} \times 4 \times 3 = 6 \text{ cm}^2
$$

#### Step 3: Total Area
$$
A_{\text{total}} = 50 + 6 = 56.00 \text{ cm}^2
$$

So, Area = 56.00 cm²

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🔎 Now, let’s go through possible types of shapes in your worksheet:

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#### 🔹 Shape 2: Quarter Circle + Rectangle?
If it’s a three-quarter circle or a semicircle with a missing sector, break it down:
- Suppose radius = 4 cm
- If it’s a three-quarters of a circle:
$$
A = \frac{3}{4} \times \pi r^2 = \frac{3}{4} \times 3.14 \times 16 = 37.68 \text{ cm}^2
$$

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#### 🔹 Shape 3: Trapezoid with Curved Side?
Possibly a rectangle with a quarter-circle on one side:
- Rectangle: 10 × 6 = 60
- Quarter circle: $ \frac{1}{4} \pi r^2 = \frac{1}{4} \times 3.14 \times 9 = 7.065 $
- Total ≈ 67.07 cm²

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#### 🔹 Shape 4: Irregular Pentagon
Split into:
- A trapezoid and a triangle
- Or two triangles and a rectangle

Use coordinates or split vertically/horizontally.

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#### 🔹 Shape 5: Rectangle with Semicircle on Top
This is common:
- Rectangle: length = 10, height = 6 → $ 10 \times 6 = 60 $
- Semicircle: diameter = 10 → radius = 5
$$
A_{\text{semi}} = \frac{1}{2} \pi r^2 = \frac{1}{2} \times 3.14 \times 25 = 39.25
$$
- Total: $ 60 + 39.25 = 99.25 \text{ cm}^2 $

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#### 🔹 Shape 6: Rectangle with a Triangular Cutout
- Full rectangle: say 12 × 8 = 96
- Triangle cutout: base 4, height 3 → $ \frac{1}{2} \times 4 \times 3 = 6 $
- Area = 96 − 6 = 90.00 cm²

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❗ Important Notes:

- Always double-check units (cm, m, etc.)
- Use π ≈ 3.14 unless otherwise specified
- Round only at the end of calculation

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✔ Final Tip:

To get accurate answers, please provide clearer details or measurements from the worksheet (e.g., lengths, radii, angles), and I can give exact solutions for each shape.

Alternatively, if you can describe or write down the dimensions of any specific shape, I’ll solve it step-by-step!

Let me know how you'd like to proceed!