The figure consists of a rectangle and two semicircles. Let's break down how to find the perimeter of this shape.

Step-by-Step Explanation:

1. Rectangle's Contribution:

   • The length of the rectangle is $8$ units.
   • The height of the rectangle (which matches the diameter of the semicircles) is $6$ units.
   • The perimeter of the rectangle without the semicircles would be $2 \times (\text{length} + \text{height}) = 2 \times (8 + 6) = 28$, but since we only care about the two horizontal sides (length), we have $2 \times 8 = 16$ units.

2. Semicircles' Contribution:

   • There are two semicircles that together form a full circle.
   • The diameter of each semicircle is $6$ units, so the radius is $\frac{6}{2} = 3$ units.
   • The circumference of a full circle is $2\pi r$, where $r$ is the radius. Thus, for a full circle with radius 3, the circumference is: $2\pi(3) = 6\pi \approx 18.8496 \text{ units}$

Total Perimeter:

• Combine the contributions from the rectangle and the full circle formed by the two semicircles: $\text{Total Perimeter} = 16 + 18.8496 \approx 34.8 \text{ units (rounded to the nearest tenth)}.$

The perimeter of the figure is approximately 34.8 units.

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Related Questions:

1. How would you calculate the area of this figure?
2. What if the diameter of the semicircles was different—how would that affect the total perimeter?
3. Can you derive the formula for the perimeter of this specific shape?
4. What would the perimeter be if only one semicircle was attached to the rectangle?
5. How would you approach this problem if the shape included quarter circles instead?

Tip:

For composite shapes, breaking them down into familiar geometric components (like rectangles and circles) simplifies both area and perimeter calculations.