https://file.aiquickdraw.com/mathbot/file/1726749479030qiypb7b5.jpg

The given shape appears to be a combination of a rectangle and a semicircle on one of its sides. Let's break it down into two parts to calculate the total area:

1. **Area of the rectangle:**
   - The width is 10 cm.
   - The length is 10.5 cm.

   The area of a rectangle is given by:
   \[
   A_{\text{rect}} = \text{width} \times \text{length}
   \]
   \[
   A_{\text{rect}} = 10 \times 10.5 = 105 \, \text{cm}^2
   \]

2. **Area of the semicircle:**
   - The diameter of the semicircle is the same as the width of the rectangle, which is 10 cm. Therefore, the radius \( r \) is:
   \[
   r = \frac{10}{2} = 5 \, \text{cm}
   \]

   The area of a full circle is:
   \[
   A_{\text{circle}} = \pi r^2
   \]
   For a semicircle, the area is half of the circle:
   \[
   A_{\text{semicircle}} = \frac{1}{2} \times \pi r^2 = \frac{1}{2} \times \pi \times (5^2) = \frac{25\pi}{2} \, \text{cm}^2
   \]

   Using \( \pi \approx 3.1416 \):
   \[
   A_{\text{semicircle}} = \frac{25 \times 3.1416}{2} = 39.27 \, \text{cm}^2
   \]

3. **Total area:**
   \[
   A_{\text{total}} = A_{\text{rect}} + A_{\text{semicircle}} = 105 + 39.27 = 144.27 \, \text{cm}^2
   \]

Thus, the total area of the figure is approximately **144.27 cm²**.

Would you like more details or have any other questions?

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Here are 5 related questions:
1. How would the area change if the width of the rectangle was doubled?
2. What would be the perimeter of this composite figure?
3. Can you generalize the formula for any such figure combining a rectangle and a semicircle?
4. How would the area calculation change if the semicircle was replaced by a quarter circle?
5. What is the effect on the area if the radius of the semicircle is increased by 20%?

**Tip:** In composite shapes, break the figure into familiar shapes like rectangles, triangles, and circles for easier calculations.

Learn how to calculate the area of a composite figure combining a rectangle and a semicircle. This problem involves the use of geometry formulas for rectangles and semicircles and is suitable for students in Grades 7-9.

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