The triangle is formed by joining the mid-points of the sides AB,BC and CA of `triangle ABC`and the area of `triangle PQR` is `6cm^2`, then the area of `triangle ABC` is :

Options

A. `36cm^2`
B. `12cm^2`
C. `18cm^2`
D. `24cm^2`

Answer

To find the area of triangle ABC given that the area of triangle PQR (formed by joining the midpoints of triangle ABC) is 6 cm², we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Relationship**:
Triangle PQR is formed by connecting the midpoints of the sides of triangle ABC. When midpoints are connected, the resulting triangle (PQR) is similar to triangle ABC and its area is one-fourth of the area of triangle ABC.

2. **Setting Up the Equation**:
Let the area of triangle ABC be denoted as \( A_{ABC} \). According to the properties of triangles formed by midpoints:
\[ A_{PQR} = \frac{1}{4} A_{ABC} \]

3. **Substituting Known Values**:
We know from the problem statement that:
\[ A_{PQR} = 6 \text{ cm}^2 \]
Substituting this into our equation gives:
\[ 6 = \frac{1}{4} A_{ABC} \]

4. **Solving for Area of Triangle ABC**:
To find \( A_{ABC} \), we can multiply both sides of the equation by 4:
\[ A_{ABC} = 6 \times 4 \]
\[ A_{ABC} = 24 \text{ cm}^2 \]

5. **Conclusion**:
Therefore, the area of triangle ABC is \( 24 \text{ cm}^2 \).

### Final Answer:
The area of triangle ABC is \( 24 \text{ cm}^2 \).