https://file.aiquickdraw.com/mathbot/file/1723948389465mjbhp5rd.jpg

To find the area of the shape provided in the image, we need to break it down into simpler parts:

1. **Identify the components:**
   - The shape consists of two rectangles and a quarter-circle segment.

2. **Dimensions from the image:**
   - The longer rectangle has dimensions \( 300 \, \text{cm} \times 17.1 \, \text{cm} \).
   - The shorter rectangle is \( 98.74 \, \text{cm} \times 17.1 \, \text{cm} \).
   - The quarter-circle has a radius of \( 17.1 \, \text{cm} \), which corresponds to the width of the rectangles.

3. **Calculate the areas:**

   - **Area of the longer rectangle:**
     \[
     A_1 = 300 \, \text{cm} \times 17.1 \, \text{cm} = 5130 \, \text{cm}^2
     \]
   
   - **Area of the shorter rectangle:**
     \[
     A_2 = 98.74 \, \text{cm} \times 17.1 \, \text{cm} = 1687.454 \, \text{cm}^2
     \]
   
   - **Area of the quarter-circle:**
     \[
     A_3 = \frac{1}{4} \times \pi \times (17.1 \, \text{cm})^2 = \frac{1}{4} \times \pi \times 292.41 \, \text{cm}^2 \approx 229.862 \, \text{cm}^2
     \]

4. **Total area:**
   \[
   \text{Total Area} = A_1 + A_2 + A_3 = 5130 \, \text{cm}^2 + 1687.454 \, \text{cm}^2 + 229.862 \, \text{cm}^2 \approx 7047.316 \, \text{cm}^2
   \]

So, the total area of the shape is approximately **7047.316 cm²**.

Would you like more details or have any questions?

### Related Questions:
1. What is the perimeter of the entire shape?
2. How would the area change if the quarter-circle were a half-circle?
3. Can the same shape be constructed with different dimensions to get a similar area?
4. How does the area change if the radius of the quarter-circle is doubled?
5. What if the shape is scaled down by half, what would be the new area?

### Tip:
When dealing with composite shapes, breaking them into smaller, recognizable shapes simplifies the process of calculating areas and perimeters.

Learn how to calculate the area of a composite shape consisting of two rectangles and a quarter-circle segment. Includes step-by-step calculations for each component and the total area. Suitable for advanced high school students and those interested in geometry and area calculations.

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