What is the area of triangle LMN with sides measuring 3 square units, 4 square units, and 5 square units?

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.

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