The centroid of a triangle `Delta ABC` is G. If the area of `DeltaABC = 72` sq. units, then the area of `Delta BGC` is

Options

A. 16 sq. units
B. 24 sq. units
C. 36 sq. units
D. 48 sq. units

Answer

To find the area of triangle BGC given that the area of triangle ABC is 72 square units, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Centroid**: The centroid (G) of a triangle divides it into six smaller triangles of equal area. This is a key property of centroids in triangles.

2. **Total Area of Triangle ABC**: We know that the total area of triangle ABC is given as 72 square units.

3. **Dividing the Area**: Since the centroid divides the triangle into six equal areas, we can denote the area of each of these smaller triangles as \( x \). Therefore, the total area of triangle ABC can be expressed as:
\[ \text{Area of } \Delta ABC = 6x \]
Given that the area is 72 square units, we have:
\[ 6x = 72 \]

4. **Calculating x**: To find \( x \), we divide both sides of the equation by 6:
\[ x = \frac{72}{6} = 12 \]

5. **Finding the Area of Triangle BGC**: The area of triangle BGC consists of two of these smaller triangles (BGA and BGC). Therefore, the area of triangle BGC can be expressed as:
\[ \text{Area of } \Delta BGC = 2x \]
Substituting the value of \( x \):
\[ \text{Area of } \Delta BGC = 2 \times 12 = 24 \text{ square units} \]

6. **Final Answer**: Thus, the area of triangle BGC is 24 square units.

### Summary:
The area of triangle BGC is **24 square units**.