If O is the centroid and AD, BE and CF are the three medians of `Delta ABC` with an area of `96 cm^(2)` then the area of `Delta BOD` in `cm^(2)` is

Options

A. 8
B. 12
C. 16
D. 24

Answer

To find the area of triangle BOD when O is the centroid of triangle ABC, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Properties of the Centroid**: The centroid (O) of a triangle divides it into six smaller triangles of equal area when medians are drawn from each vertex to the midpoint of the opposite side.

2. **Identify the Area of Triangle ABC**: We are given that the area of triangle ABC is 96 cm².

3. **Calculate the Area of Triangle BOD**: Since the centroid divides triangle ABC into six smaller triangles of equal area, the area of triangle BOD will be one-sixth of the area of triangle ABC.

\[ \text{Area of } \triangle BOD = \frac{\text{Area of } \triangle ABC}{6} \]

4. **Substitute the Given Area**: Now, substitute the area of triangle ABC into the equation.

\[ \text{Area of } \triangle BOD = \frac{96 \text{ cm}^2}{6} \]

5. **Perform the Division**:

\[ \text{Area of } \triangle BOD = 16 \text{ cm}^2 \]

### Final Answer:
The area of triangle BOD is **16 cm²**.

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