If area of ' formed by joining mid-points of the sides of `Delta ABC` is 2sq. Units. Then are of `Delta ABC` =
(a)8
(b)4
(c)2
(d)1

Options

A. 8
B. 4
C. 2
D. 1

Answer

To find the area of triangle ABC given that the area formed by joining the midpoints of its sides (triangle DEF) is 2 square units, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Relationship**:
When the midpoints of the sides of a triangle are joined, they form a new triangle (DEF) whose area is always 1/4 of the area of the original triangle (ABC).

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

3. **Substituting the Given Value**:
We know from the problem that the area of triangle DEF is 2 square units. Therefore, we can substitute this value into our equation:
\[ 2 = \frac{1}{4} A \]

4. **Solving for A**:
To find \( A \), we multiply both sides of the equation by 4:
\[ A = 2 \times 4 \]
\[ A = 8 \]

5. **Conclusion**:
Thus, the area of triangle ABC is 8 square units.

### Final Answer:
The area of triangle ABC is **8 square units** (Option A).

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