To find the perimeter of the composite figure made up of a semicircle and a triangle, we'll calculate the perimeter by adding the lengths of all the outer sides of the figure.

Step 1: Semicircle's Perimeter

The semicircle has a diameter of 14 inches.

• Radius $r$ is half of the diameter: $r = \frac{14}{2} = 7 \text{ inches}$
• The circumference of a full circle is $2\pi r$. For a semicircle, it's half of that plus the diameter: $\text{Perimeter of semicircle} = \pi r + \text{diameter} = \frac{22}{7} \times 7 + 14 = 22 + 14 = 36 \text{ inches}$

Step 2: Triangle's Perimeter

The triangle has two sides each of 15 inches, and the third side is the diameter of the semicircle, 14 inches:

• Total perimeter of the triangle: $15 + 15 + 14 = 44 \text{ inches}$

Step 3: Total Perimeter of the Composite Figure

• Since the semicircle's diameter is already counted within the triangle, we exclude it when summing: $\text{Total Perimeter} = \text{Perimeter of semicircle} + 2 \times 15 = 36 + 30 = 66 \text{ inches}$

Therefore, the approximate perimeter of the composite figure is 66 inches.

Would you like more details or have any questions?

Related Questions:

1. How do you calculate the area of a composite figure like this one?
2. What changes if the semicircle were a full circle?
3. How would the perimeter change if the triangle's sides were different lengths?
4. Can you explain how to find the perimeter of other composite shapes involving circles?
5. What is the importance of using the correct approximation for π in these calculations?

Tip: Always ensure that overlapping sides between combined shapes are not double-counted when calculating the total perimeter.