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.