1. **Problem statement:** We have a square with side length $7.4$ cm. A curved line composed of two circular arcs connects points $A$ and $B$, which lie at the midpoints of the left and right sides of the square, respectively. We need to find the area and perimeter of the shaded part of the square formed by these arcs. 2. **Understanding the figure:** - The square has side length $s = 7.4$ cm. - Points $A$ and $B$ are at the midpoints of the left and right sides, so their coordinates can be considered as $A(0, \frac{s}{2})$ and $B(s, \frac{s}{2})$. - The curved line consists of two circular arcs meeting at the midpoint of the segment $AB$. 3. **Key observations:** - The segment $AB$ is horizontal and has length $s = 7.4$ cm. - The arcs are symmetric about the horizontal line through $A$ and $B$. - The shaded region is the lower part bounded by the arcs and the square. 4. **Finding the area of the shaded region:** - The total area of the square is $$s^2 = 7.4^2 = 54.76 \text{ cm}^2.$$ - The curved line divides the square into two parts. - The shaded area is the lower part under the arcs. 5. **Finding the perimeter of the shaded region:** - The perimeter consists of: - The left side of the square from bottom to $A$ (length $\frac{s}{2} = 3.7$ cm), - The right side of the square from bottom to $B$ (length $3.7$ cm), - The bottom side of the square (length $7.4$ cm), - The curved line formed by the two arcs from $A$ to $B$. 6. **Calculating the length of the curved line:** - Since the arcs are circular and symmetric, the total length of the curved line equals the sum of the lengths of the two arcs. - The problem does not provide explicit radii or arc lengths, so we assume the arcs form a semicircle with diameter $AB$. - The length of a semicircle with diameter $d = 7.4$ cm is $$\pi \times \frac{d}{2} = \pi \times 3.7 = 11.62 \text{ cm}.$$ 7. **Calculating the perimeter:** $$\text{Perimeter} = 3.7 + 3.7 + 7.4 + 11.62 = 26.42 \text{ cm}.$$ 8. **Calculating the area of the shaded region:** - The shaded region is the area of the square minus the area above the curved line. - The area above the curved line is the area of the semicircle with diameter $7.4$ cm: $$\text{Area semicircle} = \frac{\pi r^2}{2} = \frac{\pi (3.7)^2}{2} = \frac{\pi \times 13.69}{2} = 21.49 \text{ cm}^2.$$ - Therefore, the shaded area is: $$54.76 - 21.49 = 33.27 \text{ cm}^2.$$ **Final answers:** - Area $= 33.27$ cm² - Perimeter $= 26.42$ cm