The sides of a triangle are 3 cm, 4 cm and 5 cm. The area (in `cm^(2)`) of the triangle formed by joining the mid points of this triangles : 

Options

A. 6
B. 3
C. `(3)/(2)`
D. `(3)/(4)`

Answer

To find the area of the triangle formed by joining the midpoints of a triangle with sides 3 cm, 4 cm, and 5 cm, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Type of Triangle**:
- The sides of the triangle are 3 cm, 4 cm, and 5 cm. This is a right-angled triangle (since \(3^2 + 4^2 = 5^2\)).

2. **Calculate the Area of the Original Triangle**:
- The area \(A\) of a right triangle can be calculated using the formula:
\[ A = \frac{1}{2} \times \text{base} \times \text{height} \]
- Here, we can take the base as 4 cm and the height as 3 cm:
\[ A = \frac{1}{2} \times 4 \times 3 = \frac{12}{2} = 6 \text{ cm}^2 \]

3. **Determine the Area of the Triangle Formed by the Midpoints**:
- When we join the midpoints of the sides of a triangle, the new triangle formed is similar to the original triangle and its area is one-fourth of the area of the original triangle.
- Therefore, the area of the triangle formed by the midpoints is:
\[ \text{Area of midpoints triangle} = \frac{1}{4} \times \text{Area of original triangle} \]
- Substituting the area of the original triangle:
\[ \text{Area of midpoints triangle} = \frac{1}{4} \times 6 = \frac{6}{4} = 1.5 \text{ cm}^2 \]

### Final Answer:
The area of the triangle formed by joining the midpoints of the original triangle is **1.5 cm²**.