The perimeter of the rhombus is 40 cm, and the length of its diagonal AC is 16 cm, calculate the area of the inscribed circle.

1. In a rhombus, all sides are equal. So one side = 40: 4 = 10
2. Draw the second diagonal. The diagonals are mutually perpendicular and the intersection point is halved. Hence, if the diagonals intersect at the point o, then ao = 16: 2 = 8
3. Consider a rectangular triangle. By the Pythagorean theorem od square = 100-64 = 36
Od = 6, then the whole diagonal is 6 * 2 = 12
4. The area of the rhombus is equal to the half product of the diagonals. S = 12 * 18/2 = 108.
5. r = S / p, where r is the radius of the inscribed circle, S is the area of the rhombus, p is the half perimeter. r = 108/20 = 5.4
6. S circle = pi r square. The required area = 29.16 pi.
Answer: 29.16pi