Centroid of Composite Shape

Solution Steps

Areas: \[ A_1 = 4(12)=48, \; A_2 = 6(8)=48, \; A = A_1 + A_2 = 96. \]

Centroid coordinates: \[ \bar{x}_1 = 0, \; \bar{y}_1 = 10, \; \bar{x}_2 = 0, \; \bar{y}_2 = 4. \]

Overall centroid: \[ \bar{x} = 0, \qquad \bar{y} = \frac{A_1\bar{y}_1 + A_2\bar{y}_2}{A} = \frac{48(10)+48(4)}{96} = 7. \]

Final result: \[ \boxed{ (\bar{x}, \bar{y}) = (0, 7) }. \]


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