1. **State the problem:** We have four identical rectangles each measuring 8 cm by 3 cm arranged around a smaller purple square. We need to find the area of this purple square. 2. **Understand the arrangement:** The four rectangles form a larger square with the purple square in the center. Each rectangle has length 8 cm and width 3 cm. 3. **Find the side length of the larger square:** The larger square is formed by placing two rectangles side by side along one side. The total side length of the larger square is the sum of the length of one rectangle and the width of another rectangle because the rectangles are arranged around the square. 4. **Calculate the side length of the larger square:** $$\text{Side length} = 8\text{ cm} + 3\text{ cm} = 11\text{ cm}$$ 5. **Express the side length of the larger square in terms of the purple square side $s$:** The larger square side is also equal to the side of the purple square plus twice the width of one rectangle (since rectangles are on both sides): $$11 = s + 2 \times 3$$ 6. **Solve for $s$:** $$s = 11 - 6 = 5\text{ cm}$$ 7. **Calculate the area of the purple square:** $$\text{Area} = s^2 = 5^2 = 25\text{ cm}^2$$ **Final answer:** The area of the striped purple square is $25$ square centimeters.