a = 55 feet
b = 30 feet
c = 35 feet
Step 1: Calculate the semi-perimeter (S)
Semi-perimeter (S) is calculated by summing the lengths of all sides and dividing the result by 2:
S = (a + b + c) / 2
Substituting the given values:
S = (30 + 35 + 55) / 2
S = 120 / 2
S = 60 feet
Step 2: Calculate the area using Heron's formula
Area = sqrt(S × (S - a) × (S - b) × (S - c))
Substituting the given values:
Area = sqrt(60 × (60 - 55) × (60 - 30) × (60 - 35))
Area = sqrt(60 × 30 × 25 × 5)
Area = sqrt(225000)
Area ≈ 474.34 square feet
Therefore, the approximate area of the irregular triangle with sides of length a = 30 feet, b = 35 feet, and c = 55 feet is approximately 474.34 square feet.