The problem states that a triangle and a square have the same perimeter. The three sides of the triangle measure 6.1 cm, 8.2 cm, and 9.7 cm. The task is to calculate the area of the square.

Step 1: Calculate the perimeter of the triangle

The perimeter of the triangle is the sum of its sides: $\text{Perimeter of triangle} = 6.1 + 8.2 + 9.7 = 24 \, \text{cm}$

Step 2: Perimeter of the square

Since the triangle and square have the same perimeter, the perimeter of the square is also $24 \, \text{cm}$.

Step 3: Side length of the square

The square has four equal sides, so each side length is: $\text{Side length of square} = \frac{\text{Perimeter}}{4} = \frac{24}{4} = 6 \, \text{cm}$

Step 4: Area of the square

The area of the square is calculated using the formula: $\text{Area} = \text{side}^2 = 6^2 = 36 \, \text{cm}^2$

Final Answer:

The area of the square is 36 square centimeters.

Would you like further clarification on any part of this solution?

Related Questions:

1. How do you calculate the area of a triangle with given sides using Heron’s formula?
2. Can the perimeter of a triangle and square be the same if the side lengths are decimal fractions?
3. How does the perimeter formula differ for other polygons such as pentagons or hexagons?
4. What happens to the area of a square if its perimeter doubles?
5. How can the relationship between the perimeter and area of a square be explained geometrically?

Tip:

Always ensure all units in a geometric problem are consistent to avoid confusion or miscalculation.