Question

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

Explanation:

Step1: Recall Heron's formula

Let \(a = 16\), \(b=26\), \(c = 36\). First, find the semi - perimeter \(s=\frac{a + b + c}{2}\).
\[s=\frac{16+26 + 36}{2}=\frac{78}{2}=39\]

Step2: Apply Heron's formula for area

The area \(A=\sqrt{s(s - a)(s - b)(s - c)}\).
\[A=\sqrt{39(39 - 16)(39 - 26)(39 - 36)}\]
\[A=\sqrt{39\times23\times13\times3}\]
\[A=\sqrt{39\times23\times39}\]
\[A=\sqrt{39^{2}\times23}\]
\[A = 39\sqrt{23}\]
\[A\approx39\times4.796\]
\[A\approx187.0\]

Answer:

\(187.0\)