Question

what is the area of triangle def? herons formula: area = \sqrt{s(s - a)(s - b)(s - c)}

Explanation:

1. First, find the semi - perimeter \(s\):

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

1. Then, use Heron's formula \(A=\sqrt{s(s - a)(s - b)(s - c)}\):

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

Answer:

2√14 square units