https://file.aiquickdraw.com/mathbot/file/1730081953818hnuwb0do.jpg

Let's solve each part step-by-step.

### Part a: Area of the Semicircle
The formula for the area of a full circle is:
\[
\text{Area} = \pi r^2
\]
Since we have a semicircle (half of a circle), we need to divide this by 2. Given that the radius \( r \) is 9 cm:

1. Calculate the area of the full circle:
   \[
   \pi r^2 = \pi (9)^2 = 81\pi
   \]

2. Since it's a semicircle, divide by 2:
   \[
   \text{Area of semicircle} = \frac{81\pi}{2} = 40.5\pi
   \]

So, **the area of the semicircle is \( 40.5\pi \) cm²**.

### Part b: Area of the Sector
The sector has an arc length and radius, but we need to determine the angle \( \theta \) to find the area. Here’s how we can proceed:

1. **Using the Arc Length**: The arc length \( s \) of a sector is given by:
   \[
   s = r\theta
   \]
   where \( s = 40 \) cm and \( r = 20 \) cm. Solving for \( \theta \):
   \[
   \theta = \frac{s}{r} = \frac{40}{20} = 2 \text{ radians}
   \]

2. **Calculating the Sector Area**: The area \( A \) of a sector with angle \( \theta \) (in radians) is given by:
   \[
   A = \frac{1}{2} r^2 \theta
   \]
   Plugging in \( r = 20 \) cm and \( \theta = 2 \) radians:
   \[
   A = \frac{1}{2} \times 20^2 \times 2 = \frac{1}{2} \times 400 \times 2 = 400 \text{ cm}^2
   \]

So, **the area of the sector is 400 cm²**.

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If you need any further clarification, let me know!

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### Additional Practice Questions:
1. How would you find the area of a quarter circle with radius 9 cm?
2. What would the area of a sector be if the radius is doubled but the angle stays the same?
3. How would you calculate the circumference of a semicircle with a given radius?
4. If the arc length of a sector was halved, what would happen to the angle \( \theta \)?
5. How do you calculate the perimeter of a semicircle?

### Quick Tip:
For any sector calculations, remember that the angle \( \theta \) must be in radians when applying formulas involving arc length and area.

Find the area of the semicircle and the sector. Leave your answers in terms of π.

Learn how to calculate the area of a semicircle and a sector, given their radii and arc lengths. This problem covers key geometry concepts such as the area of circles, sectors, and semicircles. Suitable for Grades 9-12.

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