Trapezoid - diagonal

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

Final Answer:

S =  382.7 cm²

Step-by-step explanation:

$$\begin{gathered} S_1=164{\text{cm}}^2 \\ S\Delta ASD=164 \\ S\Delta SDC=164/3 \\ S\Delta SCB=164 \\ S\Delta ABS=?? \\ S=S\Delta ASD+S\Delta SDC+S\Delta SCB+S\Delta ABS \\ S=S_1+S_1/3+S_1=164+164/3+164=382.7{\text{cm}}^2 \end{gathered}$$

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