Question

the sides of a triangle measure 24 mi, 45 mi, and 28 mi. find its area. write your answer as an integer or as a decimal rounded to the nearest tenth. mi²

Explanation:

Step1: Calculate the semi - perimeter

The semi - perimeter \(s=\frac{a + b + c}{2}\), where \(a = 24\), \(b = 45\), \(c = 28\).
\(s=\frac{24+45 + 28}{2}=\frac{97}{2}=48.5\)

Step2: Use Heron's formula

Heron's formula for the area of a triangle is \(A=\sqrt{s(s - a)(s - b)(s - c)}\)
Substitute the values:
\(A=\sqrt{48.5(48.5 - 24)(48.5 - 45)(48.5 - 28)}\)
\(=\sqrt{48.5\times24.5\times3.5\times20.5}\)
First, calculate \(48.5\times24.5 = 1188.25\), \(3.5\times20.5=71.75\)
Then \(1188.25\times71.75=\ 85256.9375\)
\(A=\sqrt{85256.9375}\approx292.0\)

Answer:

\(292.0\)