Solutions to Square Exercises and problems

1. Area of a Square:

Solution: The area (A) of a square with a side length (s) of 12 meters is calculated as follows: A = s^2 = 12^2 = 144 square meters

2. Perimeter of a Square:

Solution: The perimeter (P) of a square with each side measuring 18 inches is given by: P = 4 * s = 4 * 18 inches = 72 inches

3. Diagonal of a Square:

Solution: The length of the diagonal (d) of a square with sides of 10 feet can be found using the diagonal formula: d = s * √2 = 10 feet * √2 ≈ 14.14 feet (rounded to two decimal places)

4. Side Length of a Square:

Solution: Given the area (A) of a square as 121 square yards, you can find the side length (s) using the square root: s = √A = √121 square yards = 11 yards

5. Square and Rectangle Comparison:

Solution: The area of a square with a side length of 6 meters is A = 6^2 = 36 square meters. The area of the rectangle is A = length * width = 8 meters * 6 meters = 48 square meters. The rectangle has a larger area.

6. Square Inside a Circle:

Solution: In a square inscribed inside a circle with radius (r), the diagonal of the square is equal to the diameter of the circle. Therefore, the side length of the square is half the diameter. Side length = r = 5 inches

7. Square Perimeter and Area Ratio:

Solution: If the perimeter (P) of a square is 24 centimeters, each side is 24 cm / 4 = 6 cm. The area (A) of the square is A = s^2 = (6 cm)^2 = 36 square centimeters. The ratio of area to perimeter is A/P = 36 cm^2 / 24 cm = 3/2.

8. Square and Diagonal Relationship:

Solution: If the length of the diagonal (d) of a square is 10 inches, you can find the side length (s) using the diagonal formula: s = d / √2 = 10 inches / √2 ≈ 7.07 inches (rounded to two decimal places)