The sides of a triangles are 3 cm, 4 cm and 5 cm, then area of triangle is :

Question

Accepted Answer

To determine the area of a triangle with sides measuring 3 cm, 4 cm, and 5 cm, we can use the fact that these side lengths form a right-angled triangle. This is because they satisfy the Pythagorean theorem: $3^2 + 4^2 = 5^2$ (i.e., $9 + 16 = 25$).

For a right-angled triangle, the area can be calculated using the formula:

$$
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
$$

In this triangle, we can consider the sides measuring 3 cm and 4 cm as the base and height, respectively. Therefore, the area is:

$$
\text{Area} = \frac{1}{2} \times 3 \, \text{cm} \times 4 \, \text{cm} = \frac{1}{2} \times 12 \, \text{cm}^2 = 6 \, \text{cm}^2
$$

Thus, the area of the triangle is $6 \, \text{cm}^2$, which corresponds to Option 1.

Now, let's explain why the other options are incorrect:

- **Option 2: $3 \, \text{cm}^2$**: This option is incorrect because it does not match the calculated area of the triangle. The calculation using the base and height of the right-angled triangle clearly shows the area is $6 \, \text{cm}^2$.

- **Option 3: $\frac{3}{2} \, \text{cm}^2$**: This option is incorrect because it represents a much smaller area than the actual area of the triangle. The correct calculation yields $6 \, \text{cm}^2$, not $\frac{3}{2} \, \text{cm}^2$.

- **Option 4: $\frac{3}{4} \, \text{cm}^2$**: This option is incorrect as it is even smaller than Option 3 and does not reflect the true area of the triangle. The correct area, as calculated, is $6 \, \text{cm}^2$.

In conclusion, Option 1 is the correct answer because it accurately represents the area of the triangle formed by the given side lengths.