Final answer:
To estimate the area of a triangular section with sides 2 meters, 6 meters, and 7 meters, you can use Heron's formula. The semi-perimeter is 7.5 meters. The estimated area of the triangle is approximately 5.56 square meters.
Step-by-step explanation:
To estimate the area of a triangular section of a farm enclosed by fences that are 2 meters, 6 meters, and 7 meters long, we can use Heron's formula. First, we calculate the semi-perimeter (s) of the triangle:
- s = (a + b + c) / 2
- s = (2 + 6 + 7) / 2
- s = 15 / 2
- s = 7.5 meters
Now, we use Heron's formula to find the area (A):
- A = √(s(s-a)(s-b)(s-c))
- A = √(7.5(7.5 - 2)(7.5 - 6)(7.5 - 7))
- A = √(7.5 * 5.5 * 1.5 * 0.5)
- A = √(30.9375)
- A ≈ 5.56 square meters
Therefore, the estimated area of the triangular section of the farm is approximately 5.56 square meters.