Question

find the area of the triangle described below. round to the nearest hundredth.
a = 16, c = 14, b = 9

Explanation:

Step1: Calculate the semi - perimeter

The semi - perimeter \(s=\frac{a + b+ c}{2}\).
Substitute \(a = 16\), \(b = 9\), \(c = 14\) into the formula:
\(s=\frac{16 + 9+14}{2}=\frac{39}{2}=19.5\)

Step2: Use Heron's formula

Heron's formula for the area of a triangle is \(A=\sqrt{s(s - a)(s - b)(s - c)}\).
Substitute \(s = 19.5\), \(a = 16\), \(b = 9\), \(c = 14\) into the formula:
\(A=\sqrt{19.5(19.5 - 16)(19.5 - 9)(19.5 - 14)}\)
\(=\sqrt{19.5\times3.5\times10.5\times5.5}\)
First, calculate \(19.5\times3.5 = 68.25\), \(10.5\times5.5 = 57.75\)
Then \(68.25\times57.75=3942.1875\)
\(A=\sqrt{3942.1875}\approx62.79\)

Answer:

\(62.79\)