Question

find the area of δuvw. write your answer as an integer or as a decimal rounded to the nearest tenth. km²

Explanation:

Step1: Use Heron's formula

Let \(a = 20\), \(b=27\), \(c = 41\). First, find the semi - perimeter \(s=\frac{a + b + c}{2}\).
\[s=\frac{20+27 + 41}{2}=\frac{88}{2}=44\]

Step2: Calculate the area

The area \(A=\sqrt{s(s - a)(s - b)(s - c)}\).
\[A=\sqrt{44(44 - 20)(44 - 27)(44 - 41)}\]
\[A=\sqrt{44\times24\times17\times3}\]
\[A=\sqrt{44\times1224}\]
\[A=\sqrt{53856}\]
\[A\approx232.1\]

Answer:

\(232.1\)