Question

find the area of the triangle.
a = 240
b = 127
c = 219
13,811.53
11,690.43
11,704.53

Explanation:

Step1: Calculate the semi - perimeter \(s\)

The formula for the semi - perimeter \(s=\frac{a + b + c}{2}\).
Substitute \(a = 240\), \(b = 127\), \(c = 219\) into the formula:
\(s=\frac{240+127 + 219}{2}=\frac{586}{2}=293\)

Step2: Use Heron's formula \(A=\sqrt{s(s - a)(s - b)(s - c)}\)

Substitute \(s = 293\), \(a = 240\), \(b = 127\), \(c = 219\) into Heron's formula:
\(A=\sqrt{293(293 - 240)(293 - 127)(293 - 219)}\)
\(=\sqrt{293\times53\times166\times74}\)
\(=\sqrt{293\times53\times(2\times83)\times(2\times37)}\)
\(=\sqrt{4\times293\times53\times83\times37}\)
\(= 2\sqrt{293\times53\times83\times37}\)
\(\approx11704.53\)

Answer:

\(11704.53\)