Let's solve this problem step by step.

The given shape

The shape is composed of:

1. A half-circle: Its diameter is equal to the side length of the equilateral triangle, which is 25 inches.
2. An equilateral triangle: Each side of the triangle is 25 inches.

Step 1: Calculate the perimeter of the half-circle

The formula for the circumference of a full circle is: $C = \pi \cdot d$ For a half-circle, the perimeter is half of the circumference: $P_{\text{half-circle}} = \frac{\pi \cdot d}{2}$ Using $\pi \approx 3.14$ and $d = 25$: $P_{\text{half-circle}} = \frac{3.14 \cdot 25}{2} = 39.25 \, \text{inches}$

Step 2: Add the length of the triangle's two sides

Since the half-circle is attached to the triangle along one side, only the other two sides of the triangle contribute to the perimeter: $P_{\text{triangle sides}} = 25 + 25 = 50 \, \text{inches}$

Step 3: Add the two components

The total perimeter is: $P_{\text{total}} = P_{\text{half-circle}} + P_{\text{triangle sides}}$ $P_{\text{total}} = 39.25 + 50 = 89.25 \, \text{inches}$

Final Answer:

The perimeter of the shape is approximately 89.25 inches.

Would you like further clarification or detailed steps on any part?

Related Questions:

1. How would the perimeter change if the diameter of the half-circle were doubled?
2. What is the area of the half-circle if the diameter is 25 inches?
3. What is the total area of this composite shape?
4. How does the perimeter calculation change if the triangle is scalene instead of equilateral?
5. How can you express the perimeter in terms of $\pi$ instead of using an approximation?

Tip:

Always double-check whether the shared edge (in this case, the base of the triangle) is excluded from the total perimeter when calculating composite shapes.