What Is The Area Of The Triangle The Numbers Are 3, 12, and 4
To find the area of a triangle given the lengths of its three sides, we can use Heron's formula.
First, calculate the semiperimeter of the triangle, which is half of the sum of the three sides:
s = (3 + 12 + 4) / 2 = 19 / 2 = 9.5
Next, use Heron's formula to calculate the area of the triangle:
Area = √(s(s-3)(s-12)(s-4))
Area = √(9.5(9.5-3)(9.5-12)(9.5-4))
Area = √(9.5(6.5)(-2.5)(5.5))
Area = √(9.5*-84.375)
Area ≈ √(-801.5625)
Area ≈ 28.32
Therefore, the area of the triangle with side lengths 3, 12, and 4 is approximately 28.32 square units.