To find the area of triangle LMN, we can use Heron’s formula. First, let’s clarify the measurements given for the sides of the triangle:
- Side a = 3 units
- Side b = 4 units
- Side c = 5 units
Now, let’s use Heron’s formula, which states:
A = √(s × (s – a) × (s – b) × (s – c))
Where ‘s’ is the semi-perimeter of the triangle, calculated as:
- s = (a + b + c) / 2
Plugging in the values:
- s = (3 + 4 + 5) / 2 = 6 units
Now we can apply Heron’s formula:
- A = √(6 × (6 – 3) × (6 – 4) × (6 – 5))
- A = √(6 × 3 × 2 × 1)
- A = √(36)
- A = 6 square units
Thus, the area of triangle LMN is 6 square units.
In summary, by applying Heron’s formula to our triangle with sides measuring 3, 4, and 5 units, we determined the area to be 6 square units. This method is reliable and useful for calculating the area of any triangle when you know the lengths of all three sides.