Question

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

Explanation:

Step1: Calculate semi - perimeter

Let \(a = 24\), \(b = 27\), \(c = 28\). The semi - perimeter \(s=\frac{a + b + c}{2}=\frac{24+27 + 28}{2}=\frac{79}{2}=39.5\).

Step2: Apply Heron's formula

The area \(A=\sqrt{s(s - a)(s - b)(s - c)}=\sqrt{39.5(39.5 - 24)(39.5 - 27)(39.5 - 28)}=\sqrt{39.5\times15.5\times12.5\times11.5}=\sqrt{39.5\times(15.5\times12.5\times11.5)}=\sqrt{39.5\times(193.75\times11.5)}=\sqrt{39.5\times2228.125}=\sqrt{88011.9375}\approx296.7\).

Answer:

\(296.7\)