To find the area of triangle LMN, we can use Heron’s formula. This formula helps us calculate the area of a triangle when we know the lengths of all three sides.
First, we need to determine the semi-perimeter (s) of the triangle. The semi-perimeter is calculated as:
s = (a + b + c) / 2
Where a, b, and c are the lengths of the sides of the triangle. For triangle LMN, the sides are 3, 4, and 6 units.
Calculating the semi-perimeter:
s = (3 + 4 + 6) / 2 = 13 / 2 = 6.5
Next, we use Heron’s formula to find the area (A):
A = √(s * (s – a) * (s – b) * (s – c))
Plugging in the values:
A = √(6.5 * (6.5 – 3) * (6.5 – 4) * (6.5 – 6))
A = √(6.5 * 3.5 * 2.5 * 0.5)
Calculating this step-by-step:
6.5 * 3.5 = 22.75
22.75 * 2.5 = 56.875
56.875 * 0.5 = 28.4375
A = √(28.4375) ≈ 5.34 square units
So, the area of triangle LMN with the given sides is approximately 5.34 square units.