Question

fall 2025 geometry b wwva right triangle relationships and trigonometry what is the area of triangle def? herons formula: area = \\(\sqrt{s(s - a)(s - b)(s - c)})

Explanation:

Step1: Calculate semi - perimeter

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

The area \(A=\sqrt{s(s - a)(s - b)(s - c)}=\sqrt{7(7 - 3)(7 - 5)(7 - 6)}=\sqrt{7\times4\times2\times1}=\sqrt{56}=2\sqrt{14}\) square units.

Answer:

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