Three medians AD, BE and CF of `Delta ABC` intersect at G. The area of `Delta ABC` is 36 sq. cm. Then the area of `Delta CGE` is

Options

A. 12 sq. cm
B. 6 sq. cm
C. 9 sq. cm
D. 18 sq. cm

Answer

To find the area of triangle CGE when the medians AD, BE, and CF of triangle ABC intersect at point G, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Properties of Medians**:
- The three medians of a triangle intersect at a point called the centroid (G). The centroid divides each median into two segments, with the segment connecting the vertex to the centroid being twice the length of the segment connecting the centroid to the midpoint of the opposite side.

2. **Area Division by Medians**:
- The area of triangle ABC is divided into six smaller triangles by the medians. Each of these triangles has equal area since the medians divide the triangle into six smaller triangles of equal area.

3. **Calculate the Area of Triangle ABC**:
- Given that the area of triangle ABC is 36 sq. cm.

4. **Determine the Area of Each Smaller Triangle**:
- Since the area of triangle ABC is divided into 6 equal parts, the area of each smaller triangle (including triangle CGE) can be calculated as:
\[ \text{Area of each smaller triangle} = \frac{\text{Area of } \Delta ABC}{6} = \frac{36 \text{ sq. cm}}{6} = 6 \text{ sq. cm} \]

5. **Identify the Area of Triangle CGE**:
- Triangle CGE is one of these smaller triangles formed by the intersection of the medians. Therefore, the area of triangle CGE is:
\[ \text{Area of } \Delta CGE = 6 \text{ sq. cm} \]

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