Question

1. find the area of the triangle abc if a = 12 m, b = 14 m, and c = 8.0 m.

Explanation:

Step1: Use Heron's formula

Heron's formula for the area of a triangle with sides \(a\), \(b\), \(c\) is \(A=\sqrt{s(s - a)(s - b)(s - c)}\), where \(s=\frac{a + b + c}{2}\) is the semi - perimeter.
First, calculate the semi - perimeter \(s\):
\(s=\frac{12+14 + 8.0}{2}=\frac{34}{2}=17\space m\)

Step2: Substitute into Heron's formula

Now, substitute \(s = 17\), \(a=12\), \(b = 14\), \(c = 8.0\) into the formula for the area:
\(A=\sqrt{17(17 - 12)(17 - 14)(17 - 8.0)}\)
\(=\sqrt{17\times5\times3\times9}\)
\(=\sqrt{17\times135}\)
\(=\sqrt{2295}\approx47.9\space m^{2}\)

Answer:

The area of triangle \(ABC\) is approximately \(48\space m^{2}\) (or more precisely \(\approx47.9\space m^{2}\))