Trapezoid - diagonal

Trapezoid has a length of diagonal AC corssed with diagonal BD in the ratio 2:1. The triangle created by points A, cross point of diagonals S and point D has area 164 cm2. What is the area of the trapezoid?

Result

S =  382.7 cm2

Solution:

$S_{\Delta ASD} = 164 \ \\ S_{\Delta SDC} = 164/3 \ \\ S_{\Delta SCB} = 164 \ \\ S_{\Delta ABS} = ?? \ \\ \ \\ S = S_{\Delta ASD} + S_{\Delta SDC} + S_{\Delta SCB} + S_{\Delta ABS} \ \\ S = 382.7 \ \text{cm}^2$

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