Multiple choice

In a $\displaystyle \triangle ABC$, G is centroid Then area of $\displaystyle \triangle AGC$ is_______of area of $\displaystyle \triangle ABC$

  1. $\displaystyle \frac{1}{2}$
  2. $\displaystyle \frac{1}{3}$
  3. $\displaystyle \frac{1}{4}$
  4. $\displaystyle \frac{2}{3}$
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B Correct answer
Explanation

The centroid divides the triangle into three smaller triangles of equal area (AGC, BGC, AGB). Each has an area equal to 1/3 of the total area.

AI explanation

The centroid of a triangle divides it into three smaller triangles (triangle AGB, triangle BGC, and triangle AGC) of equal area. Each of these triangles shares the same altitude from a vertex to the opposite side segment, and their bases are equal because the centroid bisects the median. Therefore, the area of triangle AGC is exactly one-third of the total area of triangle ABC.

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