Answer
$y_{cog} = 1.97~m$
Work Step by Step
We can find $y_{cog}$:
$y_{cog} = \frac{\sum g_i~y_i}{\sum g_i}$
$y_{cog} = \frac{(7.80)(2.00~m)+(7.60)(2.00~m)+(7.60)(4.00~m)+(7.40)(4.00~m)}{8.00+7.80+7.60+7.40+7.60+7.80}$
$y_{cog} = 1.97~m$
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