A composite figure consists of a square with a side length of 5 cm and an adjacent triangle with a base of 5 cm and a height of 4 cm. What is the perimeter of the composite figure if the triangle's other two sides are each 6 cm long?

To find the perimeter of the composite figure, which consists of a square and an adjacent triangle, we need to sum the lengths of all the external sides. Here's how to approach the problem step by step:

### Step 1: Perimeter of the square
- Since the square has a side length of \( 5 \, \text{cm} \), each side of the square is \( 5 \, \text{cm} \).
- The square contributes four sides to the figure, but note that one side of the square coincides with the base of the triangle, so it won't be part of the perimeter. Therefore, the three external sides of the square contribute \( 5 + 5 + 5 = 15 \, \text{cm} \).

### Step 2: Perimeter of the triangle
- The triangle has a base of \( 5 \, \text{cm} \), which is shared with the square, so we do not include it in the perimeter.
- The two other sides of the triangle are each \( 6 \, \text{cm} \).

### Step 3: Total perimeter
- The external sides of the composite figure are:
  - Three sides of the square: \( 5 \, \text{cm} + 5 \, \text{cm} + 5 \, \text{cm} = 15 \, \text{cm} \)
  - Two other sides of the triangle: \( 6 \, \text{cm} + 6 \, \text{cm} = 12 \, \text{cm} \)

Thus, the total perimeter is:
\[
15 \, \text{cm} + 12 \, \text{cm} = 27 \, \text{cm}
\]

### Final Answer:
The perimeter of the composite figure is **27 cm**.

Would you like more details or have any questions about the calculation?

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Here are five related questions:
1. What is the area of the composite figure?
2. How would the perimeter change if the side length of the square were doubled?
3. What would be the perimeter if the triangle were equilateral with the same base length?
4. How do you calculate the perimeter if the triangle is isosceles but with unequal sides?
5. What is the perimeter if a similar square is added on top of the triangle?

**Tip:** When dealing with composite figures, always be careful about shared sides that should not be counted in the total perimeter!

This problem guides you through calculating the perimeter of a composite figure made up of a square (5 cm sides) and a triangle (5 cm base, 6 cm sides). Learn the step-by-step approach to solving this geometry problem, perfect for students in Grades 6-8.

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