Question

find the area of △uvw. write your answer as an integer or as a decimal rounded to the nearest tenth. m²

Explanation:

Step1: Recall Heron's formula

Heron's formula for the area of a triangle with side - lengths \(a\), \(b\), and \(c\) is \(A = \sqrt{s(s - a)(s - b)(s - c)}\), where \(s=\frac{a + b + c}{2}\) (semi - perimeter). Here, \(a = 17\), \(b = 18\), \(c = 32\).
First, calculate the semi - perimeter \(s\).
\[s=\frac{17+18 + 32}{2}=\frac{67}{2}=33.5\]

Step2: Calculate the area using Heron's formula

\[A=\sqrt{33.5(33.5 - 17)(33.5 - 18)(33.5 - 32)}\]
\[A=\sqrt{33.5\times16.5\times15.5\times1.5}\]
\[A=\sqrt{33.5\times16.5\times23.25}\]
\[A=\sqrt{33.5\times383.625}\]
\[A=\sqrt{12851.4375}\]
\[A\approx113.3\]

Answer:

\(113.3\ m^{2}\)