In triangle ABC, the three medians AD, BE, and CF intersect at G (the centroid). If the area of triangle ABC is 36 sq cm, what is the area of triangle CGE (in sq cm)?

Introduction / Context:
This question tests a standard centroid (intersection of medians) area property in triangles. Medians divide a triangle into smaller regions of equal area. Specifically, the three medians together partition the original triangle into 6 small triangles of equal area. Because the centroid is the common intersection point, many sub-triangle areas become simple fractions of the total area, independent of the triangle’s exact shape. Once you know which of those 6 equal triangles corresponds to the requested region (triangle CGE), you can compute its area as a fraction of the total 36 sq cm. This is a classic geometry aptitude problem designed to reward recognizing the equal-area partition rather than doing coordinate geometry.

Given Data / Assumptions:

• AD, BE, CF are medians of triangle ABC
• They intersect at centroid G
• Total area of triangle ABC = 36 sq cm
• Medians divide triangle ABC into 6 equal-area small triangles

Concept / Approach:
Use the known result: area(ABC) is split into 6 equal parts by the medians. Triangle CGE is one of these 6 equal triangles, so its area is (1/6) of the total area.

Step-by-Step Solution:
Medians partition triangle ABC into 6 equal-area triangles So each small triangle area = (Area of ABC) / 6 Each area = 36 / 6 = 6 sq cm Triangle CGE is one such small triangle Therefore, Area of triangle CGE = 6 sq cm

Verification / Alternative check:
You can confirm using a sample coordinate triangle: choose any triangle, compute centroid G, midpoint E, then compute the area of CGE and compare to total area. The ratio always comes out 1/6, showing the result is shape-independent and purely based on median properties.

Why Other Options Are Wrong:
12 and 18 are too large and correspond to 1/3 or 1/2 of the total area, not 1/6. 9 corresponds to 1/4 of the area, which is not produced by median partitioning. 3 would be 1/12, which is smaller than any single small triangle formed by medians.

Common Pitfalls:
Assuming medians make 4 equal parts (they do not), mixing centroid with incenter, or guessing fractions without using the 6-equal-triangles fact.

Final Answer:
The area of triangle CGE is 6 sq cm.