Question

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

Explanation:

Step1: Identify Heron's formula

Heron's formula for the area of a triangle with side - lengths \(a\), \(b\), \(c\) is \(A=\sqrt{s(s - a)(s - b)(s - c)}\), where \(s=\frac{a + b + c}{2}\) (semi - perimeter). Here, \(a = 15\), \(b = 28\), \(c = 36\).

Step2: Calculate the semi - perimeter \(s\)

\[s=\frac{15 + 28+36}{2}=\frac{79}{2}=39.5\]

Step3: Calculate \((s - a)\), \((s - b)\), \((s - c)\)

\(s - a=39.5−15 = 24.5\), \(s - b=39.5−28 = 11.5\), \(s - c=39.5−36 = 3.5\)

Step4: Calculate the area \(A\)

\[A=\sqrt{39.5\times24.5\times11.5\times3.5}=\sqrt{39.5\times(24.5\times11.5\times3.5)}=\sqrt{39.5\times(281.75\times3.5)}=\sqrt{39.5\times986.125}=\sqrt{38952.9375}\approx197.4\]

Answer:

\(197.4\)