In the quadrilateral ABCD, AC ⊥ BD, points A1, B1, C1 and D1 are the midpoint of AB, BC, CD and Da respectively. If AC = 18 and BD = 20, then In the quadrilateral ABCD, AC ⊥ BD, points A1, B1, C1 and D1 are the midpoint of AB, BC, CD and Da respectively. If AC = 18 and BD = 20, the area of quadrilateral a1b1c1d1 is ()

In the quadrilateral ABCD, AC ⊥ BD, points A1, B1, C1 and D1 are the midpoint of AB, BC, CD and Da respectively. If AC = 18 and BD = 20, then In the quadrilateral ABCD, AC ⊥ BD, points A1, B1, C1 and D1 are the midpoint of AB, BC, CD and Da respectively. If AC = 18 and BD = 20, the area of quadrilateral a1b1c1d1 is ()

That quadrilateral is a diamond. According to the median theorem of triangle, the area of a1b1c1d1 is 0.5 * ac * 0.5 * BD = 18 * 0.5 * 0.5 * 20 = 90

As shown in the figure, the parallelogram ABCD with an area of 1 is successively operated as follows: in the first operation, respectively extend AB, BC, CD, Da to points A1, B1, C1, D1, so that A1B = 2Ab, B1C = 2BC, C1d = 2CD, D1A = 2ad, successively connect A1, B1, C1, D1 to obtain parallelogram a1b1c1d1, and record its area as S1; in the second operation, respectively extend A1B1, b1c1, c1d1, d1a1 to points A2, B2, C2 And D2, so that A2B1 = 2a1b1, b2c1 = 2b1c1, c2d1 = 2c1d1, d2a1 = 2a1d1, connect A2, B2, C2, D2 in sequence, and record its area as S2 According to this rule, we can get the parallelogram a5b5c5d5, then its area S5=______ ．

As shown in the figure, the area connecting BD, b1d, ∵ B1C = 2BC, ∵ b1dc is twice the area of △ DBC, and ∵ C1d = 2dc, ∵ b1c1d is twice the area of △ b1dc, and ∵ b1c1c is six times the area of △ DBC, that is, three times the area of parallelogram ABCD, and so on, the area of the other three triangles is three times the area of parallelogram, ∵ new parallelogram The area of a parallelogram is 13 times that of the original parallelogram. If this rule continues, then the area of the parallelogram a5b5c5d5 is 135