https://file.aiquickdraw.com/mathbot/file/1726686932039rqx0ep9t.jpg

The image shows a composite geometric figure that includes several components: a trapezoid in the center, flanked by two sectors of circles on either side. The angle of each sector is \( 53^\circ \), and various side lengths are provided.

### Breakdown of the figure:
- **Center trapezoid**: 
  - One parallel side has a length of 4 cm, and the other parallel side is 2 cm.
  - The height of the trapezoid is 5 cm.

- **Left sector**:
  - The radius appears to be 2 cm (since the adjacent side of the trapezoid is also 2 cm).
  - The angle is \( 53^\circ \).

- **Right sector**:
  - The radius is 4.5 cm.
  - The angle is \( 53^\circ \).

### To calculate the total area, I will compute:
1. **Area of the trapezoid** using the formula:
   \[
   A_{\text{trapezoid}} = \frac{1}{2} \times (a + b) \times h
   \]
   where \(a = 4 \, \text{cm}\), \(b = 2 \, \text{cm}\), and \(h = 5 \, \text{cm}\).

2. **Area of each sector** using the formula:
   \[
   A_{\text{sector}} = \frac{\theta}{360^\circ} \times \pi r^2
   \]
   where \( \theta = 53^\circ \) and \(r = 2 \, \text{cm}\) for the left sector and \(r = 4.5 \, \text{cm}\) for the right sector.

Let me calculate the areas now.Here are the areas of the different components of the composite figure:

1. **Area of the trapezoid**: \( 15.0 \, \text{cm}^2 \)
2. **Area of the left sector** (with radius 2 cm): \( 1.85 \, \text{cm}^2 \)
3. **Area of the right sector** (with radius 4.5 cm): \( 9.37 \, \text{cm}^2 \)

The **total area** of the entire composite figure is approximately \( 26.22 \, \text{cm}^2 \).

Would you like further clarification or details?

Here are 5 related questions to explore:
1. How do you calculate the area of a sector for different angles?
2. What is the significance of the trapezoid's height in area calculation?
3. How does changing the radius affect the area of a sector?
4. Can you determine the perimeter of this composite figure?
5. What would happen to the total area if the angle of the sectors were different?

**Tip**: When dealing with composite figures, always break them down into simpler shapes and calculate their areas separately before adding them together.

Calculate the area of the composite figure containing a trapezoid and two circle sectors, each with an angle of 53° and different radii (2 cm and 4.5 cm).

This problem involves calculating the total area of a composite figure consisting of a trapezoid and two circle sectors. The trapezoid has parallel sides of 4 cm and 2 cm with a height of 5 cm, while the sectors have radii of 2 cm and 4.5 cm, each with a central angle of 53°. Suitable for students in Grades 8-10.

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