Question

what is the area of triangle def? herons formula: area = \sqrt{s(s - a)(s - b)(s - c)} o 2\sqrt{2} square units o 2\sqrt{14} square units o 6\sqrt{22} square units o 12\sqrt{77} square units

Explanation:

Step1: Calculate semi - perimeter s

Let \(a = 3\), \(b = 5\), \(c = 6\). The semi - perimeter \(s=\frac{a + b + c}{2}=\frac{3+5 + 6}{2}=\frac{14}{2}=7\).

Step2: Apply Heron's formula

Substitute \(s = 7\), \(a = 3\), \(b = 5\), \(c = 6\) into Heron's formula \(A=\sqrt{s(s - a)(s - b)(s - c)}\). Then \(A=\sqrt{7(7 - 3)(7 - 5)(7 - 6)}=\sqrt{7\times4\times2\times1}=\sqrt{56}=2\sqrt{14}\).

Answer:

\(2\sqrt{14}\) square units