Question

find the area of the triangle described below. round to the nearest hundredth.
b = 29,a = 16,c = 17

Explanation:

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

The formula for the semi - perimeter of a triangle is \(s=\frac{a + b+ c}{2}\).
Substitute \(a = 16\), \(b = 29\), and \(c = 17\) into the formula:
\(s=\frac{16 + 29+17}{2}=\frac{62}{2}=31\)

Step2: Use Heron's formula to find the area \(A\)

Heron's formula is \(A=\sqrt{s(s - a)(s - b)(s - c)}\).
Substitute \(s = 31\), \(a = 16\), \(b = 29\), and \(c = 17\) into the formula:
\(A=\sqrt{31(31 - 16)(31 - 29)(31 - 17)}\)
\(=\sqrt{31\times15\times2\times14}\)
\(=\sqrt{31\times420}\)
\(=\sqrt{13020}\approx114.10\)

Answer:

\(114.10\)