We have a composite figure consisting of a square and a triangle. To find the perimeter, we need to determine the total length around the figure, considering the shared side between the square and triangle.

Step 1: Perimeter of the Square

• The square has a side length of 5 cm.
• The perimeter of a square is given by: $\text{Perimeter of square} = 4 \times \text{side length} = 4 \times 5 = 20 \, \text{cm}.$

However, since one side of the square is shared with the triangle, we will not count that side twice.

Step 2: Perimeter of the Triangle

• The triangle has a base of 5 cm and two other sides, each 6 cm.
• The perimeter of the triangle is given by: $\text{Perimeter of triangle} = \text{base} + 2 \times \text{other sides} = 5 + 2 \times 6 = 5 + 12 = 17 \, \text{cm}.$

Step 3: Total Perimeter of the Composite Figure

• The total perimeter of the composite figure is the perimeter of the square plus the perimeter of the triangle, minus the shared side (which is 5 cm, the base of the triangle and one side of the square).
• Thus, the total perimeter is: $\text{Total perimeter} = (20 + 17) - 5 = 37 - 5 = 32 \, \text{cm}.$

Thus, the perimeter of the composite figure is 32 cm.

Would you like more details on any step, or do you have any questions?

Here are 5 related questions to explore further:

1. How do you find the area of the composite figure?
2. What is the difference between perimeter and area?
3. How would the perimeter change if the triangle were equilateral?
4. How do you calculate the perimeter if one side of the triangle is unknown?
5. What are some properties of composite figures in geometry?

Tip: Always be careful not to count shared sides twice when calculating the perimeter of composite figures!