Area and Perimeter of Compound Shapes (H) Worksheet for 6th - 12th ... - Free Printable

It looks like you've uploaded an image containing a worksheet titled "Area and Perimeter of Compound Shapes (B)", which includes several composite geometric figures. Since I can't view or access images directly, I’ll need you to describe the shapes in the image or provide details about them (e.g., dimensions, types of shapes involved — rectangles, triangles, semicircles, etc.).

However, I can guide you through how to solve such problems generally, and then you can apply it to your specific figures.

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🔷 General Approach: Area and Perimeter of Compound Shapes

Step 1: Break the shape into simpler parts
- Identify basic shapes: rectangles, triangles, circles, semicircles, trapezoids, etc.
- Label all known dimensions.

Step 2: Calculate the area of each part
- Use standard formulas:
- Rectangle: \( A = \text{length} \times \text{width} \)
- Triangle: \( A = \frac{1}{2} \times \text{base} \times \text{height} \)
- Circle: \( A = \pi r^2 \), Semicircle: \( \frac{1}{2} \pi r^2 \)
- Trapezoid: \( A = \frac{1}{2} (b_1 + b_2) h \)

Step 3: Add areas together
- Sum the areas of individual components.

Step 4: Find the perimeter
- Add up all outer edges.
- Be careful: internal lines (where two shapes meet) are not part of the perimeter.
- For curved edges (like semicircles), use circumference formulas:
- Full circle: \( C = 2\pi r \)
- Semicircle arc: \( \pi r \)

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📌 Example Problem (Typical from Such Sheets)

Let’s suppose one of the shapes is:

> A rectangle with a semicircle on top (like a house roof).

Given:
- Rectangle: 10 cm wide, 6 cm high
- Semicircle: diameter = 10 cm → radius = 5 cm

#### ✔ Area:
- Rectangle: \( 10 \times 6 = 60 \, \text{cm}^2 \)
- Semicircle: \( \frac{1}{2} \pi r^2 = \frac{1}{2} \pi (5)^2 = \frac{25\pi}{2} \approx 39.27 \, \text{cm}^2 \)
- Total Area: \( 60 + 39.27 = 99.27 \, \text{cm}^2 \)

#### ✔ Perimeter:
- Bottom: 10 cm
- Two sides: \( 2 \times 6 = 12 \) cm
- Top: semicircular arc = \( \pi r = 5\pi \approx 15.71 \) cm
- Total Perimeter: \( 10 + 12 + 15.71 = 37.71 \, \text{cm} \)

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Now, please describe the specific shapes in your image (or type out the labels/dimensions), and I’ll walk you through solving each one step by step! For example:

> "Figure 1: A rectangle (8 cm × 4 cm) with a right triangle on top (base 8 cm, height 3 cm)."

Then I can compute area and perimeter for that.