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

Question

Accepted Answer

To determine the area of the triangle with sides 3 cm, 4 cm, and 5 cm, we can use the formula for the area of a right-angled triangle. The given sides form a Pythagorean triplet (3, 4, 5), which means the triangle is a right-angled triangle with the right angle between the sides of 3 cm and 4 cm.

The formula for the area of a right-angled triangle is:

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

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

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

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

**Explanation for why other options are incorrect:**

- **Option 2: $3 \text{ cm}^2$**  
  This option is incorrect because, as calculated above, the area of the triangle is $6 \, \text{cm}^2$, not $3 \, \text{cm}^2$. The calculation using the base and height of 3 cm and 4 cm clearly shows that the area is double this value.

- **Option 3: $\frac{3}{2} \text{ cm}^2$**  
  This option is incorrect because $\frac{3}{2} \text{ cm}^2$ is significantly less than the calculated area of $6 \, \text{cm}^2$. The formula for the area of a right-angled triangle does not yield this result for the given side lengths.

- **Option 4: $\frac{3}{4} \text{ cm}^2$**  
  This option is incorrect because $\frac{3}{4} \text{ cm}^2$ is even smaller than Option 3 and does not match the calculated area of $6 \, \text{cm}^2$. The area calculation based on the given side lengths does not support this value.

In conclusion, the correct area of the triangle is $6 \, \text{cm}^2$, which is why Option 1 is the correct answer.