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

To find the perimeter of the composite figure, we need to calculate the sum of all the outer sides.

1. **Square**:
   - Each side of the square is \(5 \, \text{cm}\), so the perimeter of the square alone would be \(4 \times 5 = 20 \, \text{cm}\), but we need to be careful to avoid double-counting shared sides with the triangle.

2. **Triangle**:
   - The triangle is adjacent to the square, and its base is also \(5 \, \text{cm}\), which is the same as one side of the square. Since they are adjacent, this side is shared and should not be counted twice.
   - The other two sides of the triangle are each \(6 \, \text{cm}\), so their total length is \(6 + 6 = 12 \, \text{cm}\).

Now, let's combine everything:
- The perimeter of the square includes 3 unshared sides: \(5 + 5 + 5 = 15 \, \text{cm}\).
- The two remaining sides of the triangle contribute \(6 + 6 = 12 \, \text{cm}\).

So, the total perimeter of the composite figure is:
\[
15 \, \text{cm} + 12 \, \text{cm} = 27 \, \text{cm}
\]

Thus, the perimeter of the composite figure is \(27 \, \text{cm}\).

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Would you like further details or have any questions?

Here are some related questions:
1. What is the area of the composite figure?
2. How would the perimeter change if the triangle's sides were different lengths?
3. How can we find the length of a diagonal of the square?
4. What would happen to the perimeter if the side of the square were doubled?
5. How does the perimeter change if a different polygon, like a pentagon, is adjacent to the square instead of a triangle?

**Tip:** Always ensure that shared sides in composite figures are not counted twice when calculating perimeter!

Learn how to find the perimeter of a composite figure made up of a square and an adjacent triangle. This detailed step-by-step solution covers geometric concepts such as perimeter, shared sides, and composite figures. Suitable for students in Grades 6-8.

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