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      Question

      If G is the centroid and AD, BE, CF are three medians of

      ∆ABC with area 216 cm 2 , then the area of ∆AGF is?
      A 12 cm² Correct Answer Incorrect Answer
      B 36 cm² Correct Answer Incorrect Answer
      C 120 cm² Correct Answer Incorrect Answer
      D 8 cm² Correct Answer Incorrect Answer

      Solution

      Meeting point of all medians AD, BE , CF is called as centroid. Always remember that, if G is centroid in ∆ ABC, In ∆ ABC, area of ∆ AGF = area of ∆ AGE = area of ∆ BGD = area of ∆BGF  = area of ∆CGE = area of ∆CGD = 1/6th of the area of ∆ABC So area of ∆AGF = 1/6 th of area of ∆ABC = 1/6 ×  216 = 36 cm 2

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