Question : In triangle ABC, AD BE and CF are the medians intersecting at point G and the area of triangle ABC is 156 cm2. What is the area (in cm2) of triangle FGE?
Option 1: 13
Option 2: 26
Option 3: 39
Option 4: 52
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Correct Answer: 13
Solution :
AD, BE and CF are the median intersecting at point G
$\therefore$ Area of joining the points D, E and F would be $\frac{1}{4}$th of $\triangle ABC$
Area of of $\triangle DEF=\frac{1}{4}\times156=39 \;cm^2$
G will be the centroid of the triangle.
Area of $\triangle FGE$ = Area of $\triangle DFG$ = Area of $\triangle DGE$ = $\frac{1}{3}$ Area of $\triangle DEF$
= $\frac{1}{3}\times 39$
= $13 \ cm^2$
Hence, the correct answer is 13.
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