To find the area of a triangle when the lengths of all three sides are known, we can use Heron’s formula. First, we need to calculate the semi-perimeter (s) of the triangle. The semi-perimeter is half the sum of the lengths of the sides:
s = (a + b + c) / 2
For our triangle:
s = (4 + 7 + 9) / 2 = 10
Next, we apply Heron’s formula, which states that the area (A) can be found with the following formula:
A = √(s × (s – a) × (s – b) × (s – c))
Now, substituting the values we have:
A = √(10 × (10 – 4) × (10 – 7) × (10 – 9))
A = √(10 × 6 × 3 × 1)
A = √(180) ≈ 13.42
Thus, the area of the triangle with sides 4, 7, and 9 is approximately 13.42 square units.