Question

6 multiple choice 1 point find the area of the triangle. a = 72 b = 74 c = 83.6 2945.07 2502.72 2500.92

Explanation:

Step1: Calculate the semi - perimeter \(s\)

The formula for the semi - perimeter of a triangle with sides \(a\), \(b\), and \(c\) is \(s=\frac{a + b + c}{2}\).
Substitute \(a = 72\), \(b = 74\), and \(c = 83.6\) into the formula:
\(s=\frac{72+74 + 83.6}{2}=\frac{229.6}{2}=114.8\)

Step2: Use Heron's formula \(A=\sqrt{s(s - a)(s - b)(s - c)}\)

Substitute \(s = 114.8\), \(a = 72\), \(b = 74\), and \(c = 83.6\) into Heron's formula:
\(A=\sqrt{114.8(114.8 - 72)(114.8 - 74)(114.8 - 83.6)}\)
\(=\sqrt{114.8\times42.8\times40.8\times31.2}\)
First, calculate \(114.8\times42.8 = 4923.44\), \(40.8\times31.2=1273.96\)
Then \(4923.44\times1273.96\approx6.2546\times10^{6}\)
\(A=\sqrt{6.2546\times10^{6}}\approx2500.92\)

Answer:

\(2500.92\)