Working through compound shape area problems by breaking them into simpler geometric shapes and adding their areas together.

Problem Analysis:

The image shows two compound shapes, and the task is to calculate their areas. Let's break down each part step by step.

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#### Shape #1: Compound Shape with a Rectangle and a Semi-Circle
The shape consists of:
1. A rectangle.
2. A semi-circle on top of the rectangle.

##### Step 1: Identify Dimensions
- The rectangle has a width of \( 8 \) ft and a height of \( 12 \) ft.
- The semi-circle has a diameter equal to the width of the rectangle, which is \( 8 \) ft. Therefore, the radius \( r \) of the semi-circle is:
\[
r = \frac{8}{2} = 4 \text{ ft}
\]

##### Step 2: Calculate the Area of the Rectangle
The area of a rectangle is given by:
\[
A_{\text{R}} = \text{base} \times \text{height}
\]
Substitute the dimensions:
\[
A_{\text{R}} = 8 \times 12 = 96 \text{ ft}^2
\]

##### Step 3: Calculate the Area of the Semi-Circle
The area of a full circle is given by:
\[
A_{\text{circle}} = \pi r^2
\]
Since we have a semi-circle, its area is half of the full circle:
\[
A_{\text{HC}} = \frac{1}{2} \pi r^2
\]
Substitute \( r = 4 \):
\[
A_{\text{HC}} = \frac{1}{2} \pi (4)^2 = \frac{1}{2} \pi \cdot 16 = 8\pi \text{ ft}^2
\]

##### Step 4: Calculate the Total Area
The total area of the compound shape is the sum of the area of the rectangle and the area of the semi-circle:
\[
\text{Total Area} = A_{\text{R}} + A_{\text{HC}}
\]
Substitute the values:
\[
\text{Total Area} = 96 + 8\pi
\]
Using \( \pi \approx 3.14 \):
\[
8\pi \approx 8 \times 3.14 = 25.12
\]
Thus:
\[
\text{Total Area} \approx 96 + 25.12 = 121.12 \text{ ft}^2
\]

##### Final Answer for Shape #1:
\[
\boxed{121.12 \text{ ft}^2}
\]

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#### Shape #2: Compound Shape with Two Triangles
The shape consists of:
1. A larger triangle at the top.
2. A smaller triangle at the bottom.

##### Step 1: Identify Dimensions
- The larger triangle has a base of \( 8 \) ft and a height of \( 7 \) ft.
- The smaller triangle has a base of \( 8 \) ft and a height of \( 4 \) ft.

##### Step 2: Calculate the Area of the Larger Triangle
The area of a triangle is given by:
\[
A_{\text{T}} = \frac{1}{2} \times \text{base} \times \text{height}
\]
For the larger triangle:
\[
A_{\text{T, large}} = \frac{1}{2} \times 8 \times 7 = \frac{1}{2} \times 56 = 28 \text{ ft}^2
\]

##### Step 3: Calculate the Area of the Smaller Triangle
For the smaller triangle:
\[
A_{\text{T, small}} = \frac{1}{2} \times 8 \times 4 = \frac{1}{2} \times 32 = 16 \text{ ft}^2
\]

##### Step 4: Calculate the Total Area
The total area of the compound shape is the sum of the areas of the two triangles:
\[
\text{Total Area} = A_{\text{T, large}} + A_{\text{T, small}}
\]
Substitute the values:
\[
\text{Total Area} = 28 + 16 = 44 \text{ ft}^2
\]

##### Final Answer for Shape #2:
\[
\boxed{44 \text{ ft}^2}
\]

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Summary of Answers:

1. Shape #1: \( \boxed{121.12 \text{ ft}^2} \)
2. Shape #2: \( \boxed{44 \text{ ft}^2} \)