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To find the area of the composite figure, we need to analyze its shape. The figure consists of a rectangle with a semicircle attached to one of its shorter sides.

Here’s the breakdown of the dimensions:
- The rectangle has a width of 8 feet and a length of 10 feet.
- The semicircle has a diameter equal to the width of the rectangle, so its diameter is 8 feet, giving it a radius of \( \frac{8}{2} = 4 \) feet.

### Steps to Find the Area
1. **Area of the Rectangle**:
   \[
   \text{Area}_{\text{rectangle}} = \text{width} \times \text{length} = 8 \, \text{ft} \times 10 \, \text{ft} = 80 \, \text{square feet}
   \]

2. **Area of the Semicircle**:
   The area of a full circle is \( \pi r^2 \). Since we have a semicircle, we divide by 2.
   \[
   \text{Area}_{\text{semicircle}} = \frac{1}{2} \pi r^2 = \frac{1}{2} \pi (4)^2 = \frac{1}{2} \pi \times 16 = 8\pi \, \text{square feet}
   \]

3. **Total Area of the Composite Figure**:
   \[
   \text{Total Area} = \text{Area}_{\text{rectangle}} + \text{Area}_{\text{semicircle}} = 80 + 8\pi \, \text{square feet}
   \]

So, the area of the composite figure in terms of \( \pi \) is:
\[
\boxed{80 + 8\pi} \, \text{square feet}
\]

Would you like further details or have any questions about this process?

### Related Questions:
1. What would the area be if the semicircle was a full circle?
2. How would the area change if the radius of the semicircle was doubled?
3. How do you calculate the perimeter of this composite figure?
4. What if the rectangle’s length was reduced to 8 feet?
5. How can we express the result in approximate decimal form instead of in terms of \( \pi \)?

### Tip:
When working with composite shapes, break down the figure into familiar shapes, like rectangles, circles, or triangles, to calculate the area more easily.

Find the area of the composite figure in terms of π.

Calculate the area of a composite figure combining a rectangle and a semicircle. This problem guides students in finding areas in terms of π using the formula for circles and rectangles. Ideal for Grades 7-9 students.

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