1. The problem involves finding the side length and area of the smaller square inscribed inside a larger square with side length 10 cm (since 100 cm² = 10²). 2. The smaller square is formed by connecting the midpoints of the sides of the larger square. 3. The side length of the larger square is 10 cm, so the midpoint of each side is 5 cm from each corner. 4. The side length of the smaller square is the distance between two adjacent midpoints of the larger square's sides. 5. This distance forms the hypotenuse of a right triangle with legs of length 5 cm each. 6. Using the Pythagorean theorem: $$s = \sqrt{5^2 + 5^2} = \sqrt{25 + 25} = \sqrt{50} = 5\sqrt{2}$$ 7. Therefore, the side length of the smaller square is $5\sqrt{2}$ cm. 8. The area of the smaller square is: $$A = s^2 = (5\sqrt{2})^2 = 25 \times 2 = 50$$ 9. So, the area of the smaller square is 50 cm².