The triangle is formed by joining the mid point of the sides AB, BC and CA of `DeltaABC` and the area of `DeltaPQR` is `6cm^(2)`, then the area of `DeltaABC` 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 the sides of triangle ABC) is 6 cm², we can use the following steps:

### Step-by-Step Solution:

1. **Understanding the Relationship**:
When a triangle is formed by joining the midpoints of another triangle's sides, the area of the new triangle (PQR) is always one-fourth the area of the original triangle (ABC). This is a property of triangles.

2. **Setting Up the Equation**:
Let the area of triangle ABC be denoted as Area(ABC). According to the property mentioned, we have:
\[ \text{Area}(PQR) = \frac{1}{4} \times \text{Area}(ABC) \]

3. **Substituting the Known Value**:
We know that the area of triangle PQR is 6 cm². Therefore, we can substitute this value into the equation:
\[ 6 = \frac{1}{4} \times \text{Area}(ABC) \]

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

5. **Final Answer**:
The area of triangle ABC is 24 cm².