The area of the polygon is length × width = (4 - 1) × (5 - 1) = 3 × 4 = 12.

The length of the diagonal can be found using the distance formula: d = √((8 - 0)² + (6 - 0)²) = √(64 + 36) = √100 = 10.

The diagonal of the square equals the diameter of the circle. Diagonal = 2 × radius = 10. Side = diagonal/√2 = 10/√2 = 5√2.

Perimeter = 2 * (length + width) = 2 * (4 + 3) = 2 * 7 = 14.

Perimeter = number of sides × side length = 6 × 4 = 24.