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?

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.