Question

find the area of △xyz. write your answer as an integer or as a decimal rounded to the nearest tenth. cm²

Explanation:

Step1: Apply Heron's formula

First, find the semi - perimeter $s$. Let $a = 16$, $b = 28$, $c = 38$. Then $s=\frac{a + b + c}{2}=\frac{16+28 + 38}{2}=\frac{82}{2}=41$.

Step2: Calculate the area

The area $A=\sqrt{s(s - a)(s - b)(s - c)}=\sqrt{41(41 - 16)(41 - 28)(41 - 38)}=\sqrt{41\times25\times13\times3}=\sqrt{41\times975}=\sqrt{39975}\approx199.9$.

Answer:

$199.9$ cm²