The perimeter of a composite figure is the sum of the lengths of its outer sides.

In this case, we have a square and a triangle sharing a side. Here's how we calculate the perimeter:

1. Square:

   • Each side of the square is 5 cm.
   • The square has four sides, but one of its sides is adjacent to the triangle's base, so we don't count that side twice in the perimeter.
   • For the square's contribution to the perimeter, we count 3 sides: $5 \, \text{cm} + 5 \, \text{cm} + 5 \, \text{cm} = 15 \, \text{cm}$

2. Triangle:

   • The base of the triangle is 5 cm (which is the same as one side of the square, so it's already counted).
   • To find the length of the triangle's other two sides, we first need the hypotenuse. The height of the triangle is 4 cm, and using the Pythagorean theorem: $\text{Hypotenuse} = \sqrt{(5^2 + 4^2)} = \sqrt{(25 + 16)} = \sqrt{41} \approx 6.4 \, \text{cm}$
   • The third side is the height of the triangle, which is 4 cm.

3. Total Perimeter:

   • Sum up the outer sides: $15 \, \text{cm} + 4 \, \text{cm} + 6.4 \, \text{cm} = 25.4 \, \text{cm}$

Thus, the perimeter of the composite figure is approximately 25.4 cm.

Would you like more details or have any other questions?

Here are 5 related questions for further exploration:

1. How would the perimeter change if the triangle's height were doubled?
2. Can you calculate the area of this composite figure?
3. What happens to the perimeter if the base of the triangle is halved?
4. How do you find the perimeter if the triangle is an equilateral one?
5. How does the Pythagorean theorem apply to finding side lengths of triangles?

Tip: When dealing with composite figures, always account for shared sides to avoid counting them twice in the perimeter calculation.