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Let's break down the problem to calculate the area of the given figure, which consists of an isosceles trapezoid and a semicircle.

### Step 1: Area of the trapezoid
For an isosceles trapezoid, the formula for the area is:

\[
A_{\text{trapezoid}} = \frac{1}{2} \times (b_1 + b_2) \times h
\]

Where:
- \(b_1 = 10\) (the base of the trapezoid)
- \(b_2 = 14\) (the top of the trapezoid)
- \(h = 12\) (the height of the trapezoid)

Substitute these values into the formula:

\[
A_{\text{trapezoid}} = \frac{1}{2} \times (10 + 14) \times 12 = \frac{1}{2} \times 24 \times 12 = 144
\]

Thus, the area of the trapezoid is **144 square units**.

### Step 2: Area of the semicircle
The semicircle is attached to the base of the trapezoid. The diameter of the semicircle is equal to the base of the trapezoid, \(10\). The radius of the semicircle is:

\[
r = \frac{10}{2} = 5
\]

The area of a full circle is given by \(A = \pi r^2\), so the area of the semicircle is half of that:

\[
A_{\text{semicircle}} = \frac{1}{2} \times \pi \times r^2 = \frac{1}{2} \times \pi \times 5^2 = \frac{1}{2} \times \pi \times 25 = 12.5\pi
\]

Using \(\pi \approx 3.1416\):

\[
A_{\text{semicircle}} \approx 12.5 \times 3.1416 \approx 39.3
\]

Thus, the area of the semicircle is approximately **39.3 square units**.

### Step 3: Total area of the figure
The total area of the figure is the sum of the area of the trapezoid and the area of the semicircle:

\[
A_{\text{total}} = A_{\text{trapezoid}} + A_{\text{semicircle}} = 144 + 39.3 = 183.3
\]

### Final Answer:
The total area of the figure is approximately **183.3 square units**, rounded to the nearest tenth.

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Would you like any additional details or explanations?

### Follow-up questions:
1. How is the formula for the area of a trapezoid derived?
2. Why is the area of a semicircle half that of a full circle?
3. Can this approach be used for other combinations of geometric shapes?
4. How would the calculation change if the shape was a full circle instead of a semicircle?
5. What happens to the area if the dimensions of the trapezoid change?

### Tip:
Always check if the given shapes share any dimensions (like the base in this case), as it simplifies calculations.

Find the area of the figure below, composed of an isosceles trapezoid and one semicircle. Rounded to the nearest tenths place.

Learn how to find the area of a combined shape that includes an isosceles trapezoid and a semicircle with specific dimensions. This problem involves key geometry concepts and is suitable for students in Grades 6-8. The solution includes step-by-step calculations using area formulas.

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