If the perimeter of the diamond is 40 cm and the ratio of the degrees of two adjacent internal angles is 1:2, the area of the diamond is 40 cm___ cm.

If the perimeter of the diamond is 40 cm and the ratio of the degrees of two adjacent internal angles is 1:2, the area of the diamond is 40 cm___ cm.

As shown in the figure, ab = 40 △ 4 = 10cm, ∵ the ratio of degree of two adjacent internal angles is 1:2, ∵ bad = 11 + 2 × 180 ° = 60 °, ∵ abd is an equilateral triangle, ∵ BD = AB = 10cm, ∵ Bo = 12 × 10 = 5cm, in RT △ ABO, Ao = ab2-bo2 = 102-52 = 53cm, ∵ AC = 2ao = 2 × 53 = 103cm, ∵ rhombic