Question

find the area of the triangle described below. round to the nearest hundredth.
c = 18,b = 29,a = 27

Explanation:

Step1: Calculate the semi - perimeter

The semi - perimeter \(s=\frac{a + b+ c}{2}\).
Substitute \(a = 27\), \(b = 29\), \(c = 18\) into the formula:
\(s=\frac{27+29 + 18}{2}=\frac{74}{2}=37\)

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 \(s = 37\), \(a = 27\), \(b = 29\), \(c = 18\) into the formula:
\(A=\sqrt{37(37 - 27)(37 - 29)(37 - 18)}\)
\(=\sqrt{37\times10\times8\times19}\)
\(=\sqrt{37\times10\times152}\)
\(=\sqrt{37\times1520}\)
\(=\sqrt{56240}\approx237.15\)

Answer:

\(237.15\)