In triangle ABC, medians AD, BE, and CF intersect at centroid G. If area(ΔABC) = 36 cm^2, find area(ΔCGE).

Introduction / Context:Medians of a triangle intersect at the centroid, partitioning the triangle into six smaller triangles of equal area. Recognizing this partition lets us read off areas of sub-triangles like ΔCGE directly.

Given Data / Assumptions:

• AD, BE, CF are medians; E is midpoint of AC.
• G is the centroid (intersection of the three medians).
• Area(ΔABC) = 36 cm^2.

Concept / Approach:Centroid divides the triangle into six equal-area small triangles formed by the three medians. Thus each small triangle has area (total area)/6.

Step-by-Step Solution:

Verification / Alternative check:Draw medians; around each vertex, two small triangles meet; all six are congruent in area by symmetry and midpoint properties.

Why Other Options Are Wrong:

• 9, 12, 18: These assume thirds or halves, not sixths.

Common Pitfalls:Forgetting that three medians create 6, not 4, parts; confusing centroid 2:1 segment property with area partition.

Final Answer:6 sq cm