https://file.aiquickdraw.com/mathbot/file/1730311425290t97socyc.jpg

To solve this, let’s divide the shape into two parts: a rectangle and a half-circle, then add the areas of each.

1. **Rectangle Area**:
   - The rectangle's dimensions are 7 cm (length) and 6 cm (height).
   - Area of rectangle = length × height = \( 7 \, \text{cm} \times 6 \, \text{cm} = 42 \, \text{cm}^2 \).

2. **Half-Circle Area**:
   - The half-circle’s diameter is the same as the rectangle's height, which is 6 cm. Thus, the radius \( r = \frac{6 \, \text{cm}}{2} = 3 \, \text{cm} \).
   - Area of a full circle = \( \pi r^2 \).
   - For the half-circle, Area = \( \frac{1}{2} \pi r^2 \).
   - Substitute \( \pi = 3.14 \) and \( r = 3 \, \text{cm} \):
     \[
     \text{Half-circle Area} = \frac{1}{2} \times 3.14 \times (3)^2 = \frac{1}{2} \times 3.14 \times 9 = 14.13 \, \text{cm}^2
     \]

3. **Total Area**:
   - Add the area of the rectangle and the half-circle:
     \[
     \text{Total Area} = 42 \, \text{cm}^2 + 14.13 \, \text{cm}^2 = 56.13 \, \text{cm}^2
     \]

**Answer**: \( 56.13 \, \text{cm}^2 \).

Would you like a further breakdown of any part of this solution?

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Here are related questions you might find useful:

1. What would the area be if the half-circle were a full circle?
2. How would the area change if the diameter of the half-circle was 8 cm?
3. What is the perimeter of this shape?
4. How does using a more accurate value of \( \pi \) (like 3.14159) affect the area calculation?
5. How can we find the area if the shape was scaled by a factor of 2?

**Tip**: When dealing with composite shapes, breaking them into simpler parts often makes area calculations easier.

Find the area enclosed by the figure. Use 3.14 for π and do not round your answer. (The figure is not to scale).

Learn how to find the area of a composite shape consisting of a rectangle and a half-circle using geometry formulas. This problem covers area calculation for composite shapes, specifically adding the areas of a rectangle and half-circle. Suitable for students in Grades 7-9.

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