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From the image you provided, it seems that the problem involves finding expressions for the area of various composite shapes based on the areas of two given basic shapes: one square shape with an area \( a \) and one semicircle shape with an area \( b \). Let's break it down step by step.

### Given Information:
- The square shape (marked as "area \( a \)") has an area of \( a \).
- The semicircle shape (marked as "area \( b \)") has an area of \( b \).

### Let's now find the area for each composite shape (labeled from a) to g)):

1. **Shape a)**: This shape is a semicircle (area \( b \)). Since this is directly the given semicircle, the area is simply:
   \[
   \text{Area of shape a)} = b
   \]

2. **Shape b)**: This shape is a full circle, which can be constructed by combining two semicircles. Since each semicircle has an area \( b \), the area of the full circle is:
   \[
   \text{Area of shape b)} = 2b
   \]

3. **Shape c)**: This shape consists of four semicircles arranged in a grid. The total area is the sum of the four semicircles, so:
   \[
   \text{Area of shape c)} = 4b
   \]

4. **Shape d)**: This shape looks like a cross made of one full circle in the center and four semicircles attached at the edges. The area consists of:
   - The central circle (which has an area of \( 2b \)).
   - Four semicircles, each with an area \( b \).
   
   So, the total area is:
   \[
   \text{Area of shape d)} = 2b + 4b = 6b
   \]

5. **Shape e)**: This shape consists of a square with two semicircles attached to opposite sides. The area includes:
   - One square (area \( a \)).
   - Two semicircles (each with an area \( b \)).

   Thus, the total area is:
   \[
   \text{Area of shape e)} = a + 2b
   \]

6. **Shape f)**: This shape is a large grid consisting of 9 square units, where some parts have semicircles overlapping. The area can be broken down into:
   - Five squares, each with an area \( a \).
   - Two semicircles, each with an area \( b \).

   The total area is:
   \[
   \text{Area of shape f)} = 5a + 2b
   \]

7. **Shape g)**: This shape consists of four semicircles arranged around the corners of a square. The area is:
   - One square (area \( a \)).
   - Four semicircles, each with an area \( b \).

   Thus, the total area is:
   \[
   \text{Area of shape g)} = a + 4b
   \]

### Summary of the Area Expressions:
a) \( b \)  
b) \( 2b \)  
c) \( 4b \)  
d) \( 6b \)  
e) \( a + 2b \)  
f) \( 5a + 2b \)  
g) \( a + 4b \)

Would you like further details on any of these areas? Here are 5 related questions to consider:

1. How would the area change if the dimensions of shape \( a \) or \( b \) were doubled?
2. Can you calculate the specific numerical area if \( a \) and \( b \) were given values (e.g., \( a = 4 \) and \( b = 2 \))?
3. How could you find the perimeter for each shape, given this information?
4. What would happen to the total area if one semicircle was replaced with a full circle in shape e)?
5. How do composite shapes affect the total area in real-world applications?

**Tip**: When working with composite shapes, always break them down into simpler basic components (like squares or semicircles) to calculate areas more easily.

Find expressions for the area of the shapes below (simplify where possible). Using the given areas of a square (area = a) and a semicircle (area = b), write expressions for the area of composite shapes.

Learn how to calculate the area of composite shapes formed from squares and semicircles. Understand the concept of area by breaking down complex figures into simpler ones and applying basic geometry formulas. Suitable for Grades 6-8.

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