The shape in the image is a combination of a rectangle and two semicircles at the top and bottom. Here's how to calculate the area:

1. Area of the rectangle:

• The width of the rectangle is $9 \, \text{cm}$, and the height is the same as the distance between the centers of the semicircles, $9.3 \, \text{cm}$.

$\text{Area of rectangle} = \text{width} \times \text{height} = 9 \times 9.3 = 83.7 \, \text{cm}^2$

2. Area of the semicircles:

• The two semicircles together form a full circle with a diameter of $9 \, \text{cm}$, which means the radius is $\frac{9}{2} = 4.5 \, \text{cm}$.

$\text{Area of a full circle} = \pi \times r^2 = \pi \times (4.5)^2 = 20.25\pi \approx 63.62 \, \text{cm}^2$

3. Total area:

• To find the total area, add the area of the rectangle and the area of the full circle:

$\text{Total area} = 83.7 + 63.62 = 147.32 \, \text{cm}^2$

Thus, the total colored area is approximately 147.32 cm².

Would you like further details or have any questions?

Here are five related questions you might find useful:

1. How do you calculate the perimeter of this shape?
2. What is the area if the radius of the semicircles changes?
3. How does changing the height of the rectangle affect the total area?
4. Can the total area be expressed in terms of algebraic variables instead of specific numbers?
5. How can this shape be generalized for different kinds of curved shapes?

Tip: When calculating the area of composite shapes, break the shape into familiar parts like rectangles and circles.