Trapezoid - central median

The central median divides the trapezoid into two smaller trapezoids. Find the ratio of its areas.

Result

p = (Correct answer is: (3a+c)/(a+3c))

Step-by-step explanation:

$$\begin{gathered} S_1=((a+c)\mathrm{/}2+c)h\mathrm{/}2 \\ {S}_2=((a+c)\mathrm{/}2+a)h\mathrm{/}2 \\ p=S_2:S_1=((a+c)\mathrm{/}2+a)\mathrm{/}((a+c)\mathrm{/}2+c) \\ p=(1.5a+0.5c)\mathrm{/}(0.5a+1.5c) \\ p=(3a+c)\mathrm{/}(a+3c) \end{gathered}$$

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