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 side lengths \(a\), \(b\), 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 to find the area \(A\)

Heron's formula is \(A=\sqrt{s(s - a)(s - b)(s - c)}\)
Substitute \(s = 114.8\), \(a = 72\), \(b = 74\), and \(c = 83.6\) into the formula:
\(A=\sqrt{114.8(114.8 - 72)(114.8 - 74)(114.8 - 83.6)}\)
\(=\sqrt{114.8\times42.8\times40.8\times31.2}\)
\(=\sqrt{114.8\times(42.8\times40.8\times31.2)}\)
First, calculate \(42.8\times40.8 = 1746.24\), then \(1746.24\times31.2=54482.688\)
Then \(114.8\times54482.688 = 6250000.6864\)
\(A=\sqrt{6250000.6864}\approx2500.92\)

Answer:

\(2500.92\)