To calculate the area of the blue shape in the image, let's analyze the different parts that make up the shape.

The shape appears to be composed of the following components:

1. A quarter-circle on the left: This is the leftmost curved part of the shape.
2. A semicircle in the middle: This is the upper curved part of the shape.
3. A right triangle on the right: This is the rightmost part of the shape.

Step-by-Step Area Calculation

1. Quarter-Circle Area:

   • The area of a quarter-circle is given by: $A_1 = \frac{1}{4} \times \pi r^2$ where $r$ is the radius of the quarter-circle.

2. Semicircle Area:

   • The area of a semicircle is given by: $A_2 = \frac{1}{2} \times \pi r^2$ where $r$ is the radius of the semicircle.

3. Right Triangle Area:

   • The area of a right triangle is given by: $A_3 = \frac{1}{2} \times \text{base} \times \text{height}$

Total Area Calculation

The total area $A_{\text{total}}$ of the shape is the sum of these areas: $A_{\text{total}} = A_1 + A_2 + A_3$

To calculate the precise area, I'll need the dimensions of the shape, such as the radii of the quarter-circle and semicircle, as well as the base and height of the triangle. These might be indicated by the horizontal and vertical lines in the image. If you provide these dimensions, I can calculate the exact area for you.

Would you like to provide those measurements, or should I make assumptions based on a possible standard size?

---

Related Questions:

1. How does changing the radius of the semicircle affect the total area?
2. What happens to the total area if the right triangle's height is doubled?
3. How would the area calculation change if the shape was mirrored?
4. What if the quarter-circle and semicircle were replaced with full circles?
5. How can this shape be divided into simpler geometric figures for easier calculations?

Tip: When dealing with composite shapes, breaking them down into standard geometric figures (like circles, triangles, rectangles) simplifies area calculations significantly.