Question : Three medians AD, BE, and CF of $\triangle ABC$ intersect at G. The area of $\triangle ABC$ is $36\text{ cm}^2$. Then the area of $\triangle CGE$ is:
Option 1: $12\text{ cm}^2$
Option 2: $6\text{ cm}^2$
Option 3: $9\text{ cm}^2$
Option 4: $18\text{ cm}^2$
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Correct Answer: $6\text{ cm}^2$
Solution : Given: AD, BE, and CF are medians of $\triangle ABC$ intersect at G. The area of $\triangle ABC$ = $36\text{ cm}^2$ The median of the triangle divides the triangle into equal areas. $\therefore$ Area of $\triangle CGE$ = $ \frac{\text{Area of} \triangle ABC }{6}=\frac{36}{6}=6\text{ cm}^2$ Hence, the correct answer is $6\text{ cm}^2$.
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Question : Suppose $\triangle ABC$ be a right-angled triangle where $\angle A=90°$ and $AD\perp BC$. If the area of $\triangle ABC =40$ cm$^{2}$ and $\triangle ACD =10$ cm$^{2}$ and $\overline{AC}=9$ cm, then the length of $BC$ is:
Question : In $\triangle$ABC, two medians BE and CF intersect at the point O. P and Q are the midpoints of BO and CO, respectively. If the length of PQ = 3 cm, then the length of FE will be:
Question : $G$ is the centroid of the equilateral triangle $ABC$. If $AB$ is $9\text{ cm}$, then $AG$ is equal to:
Question : If $\triangle ABC \sim \triangle PQR$, AB =4 cm, PQ=6 cm, QR=9 cm and RP =12 cm, then find the perimeter of $\triangle$ ABC.
Question : In $\triangle ABC$, D and E are the midpoints of sides BC and AC, respectively. AD and BE intersect at G at the right angle. If AD = 18 cm and BE=12 cm, then the length of DC (in cm ) is:
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