An isosceles triangle (two sides equal) is placed on top of a square as shown in the picture. If the two equal sides of the triangle are 19ft
 long and the square is 25ft
 on each side, what is the perimeter of the figure?

To find the perimeter of the figure, we need to sum the perimeters of the square and the isosceles triangle on top of it.

### Step 1: Perimeter of the square
Since each side of the square is 25 ft, the perimeter of the square is:
\[
\text{Perimeter of the square} = 4 \times 25 = 100 \, \text{ft}
\]

### Step 2: Base of the triangle
The isosceles triangle is placed on top of the square, meaning that the base of the triangle is the same as one side of the square, which is 25 ft.

### Step 3: Finding the remaining sides of the triangle
The two equal sides of the triangle are given as 19 ft each.

### Step 4: Total perimeter of the figure
To find the total perimeter, we need to add the two equal sides of the triangle to the perimeter of the square, but exclude the base of the triangle since it coincides with one side of the square.

So, the total perimeter is:
\[
\text{Perimeter of the figure} = \text{Perimeter of square} + 2 \times \text{Equal sides of triangle} = 100 + 2 \times 19
\]
\[
\text{Perimeter of the figure} = 100 + 38 = 138 \, \text{ft}
\]

### Final Answer:
The perimeter of the figure is **138 ft**.

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you calculate the area of the isosceles triangle on top of the square?
2. What is the height of the isosceles triangle?
3. How would the perimeter change if the side length of the square increased?
4. What if the triangle were equilateral instead of isosceles?
5. How does the Pythagorean theorem apply to this situation?

**Tip:** Always ensure that the base of the triangle is accurately aligned with the side of the square when calculating the perimeter.

An isosceles triangle (two sides equal) is placed on top of a square as shown in the picture. If the two equal sides of the triangle are 19 ft long and the square is 25 ft on each side, what is the perimeter of the figure?

Learn how to calculate the perimeter of a figure combining an isosceles triangle with two sides of 19 ft placed on top of a square with a side length of 25 ft. This problem involves geometry, focusing on the perimeter calculation of composite shapes. Suitable for students in Grades 7-9.

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