Composite Perimeter 66E835

1. **State the problem:** We need to find the distance around the figure, which is the perimeter of a composite shape made of a rectangle and a semicircle. 2. **Identify the parts:** The rectangle has height $8$ cm and width $14$ cm. The semicircle is attached to the left side of the rectangle, so its diameter is the height of the rectangle, $8$ cm. 3. **Formula for perimeter of composite figure:** The perimeter is the sum of the three sides of the rectangle (excluding the side where the semicircle is attached) plus the circumference of the semicircle. 4. **Calculate the circumference of the semicircle:** The circumference of a full circle is $$C = \pi d$$ where $d$ is the diameter. For a semicircle, the curved part length is half the circumference: $$\text{semicircle length} = \frac{\pi d}{2} = \frac{\pi \times 8}{2} = 4\pi$$ 5. **Calculate the perimeter:** The three sides of the rectangle to include are the bottom side ($14$ cm), the right vertical side ($8$ cm), and the top side ($14$ cm). So the total perimeter is: $$P = 14 + 8 + 14 + 4\pi = 36 + 4\pi$$ 6. **Final answer:** The distance around the figure is $$36 + 4\pi$$ cm, which is approximately $$36 + 4 \times 3.1416 = 36 + 12.5664 = 48.5664$$ cm. So, the perimeter is about $48.57$ cm.