Question

7 multiple choice 1 point find the area of the triangle. a = 69.4 b = 65.4 c = 48.2 1095.9 1081.8 1511.72

Explanation:

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

The formula for the semi - perimeter \(s=\frac{a + b + c}{2}\).
Substitute \(a = 69.4\), \(b = 65.4\), \(c = 48.2\) into the formula:
\(s=\frac{69.4+65.4 + 48.2}{2}=\frac{183}{2}=91.5\)

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

Substitute \(s = 91.5\), \(a = 69.4\), \(b = 65.4\), \(c = 48.2\) into Heron's formula:
\(A=\sqrt{91.5\times(91.5 - 69.4)\times(91.5 - 65.4)\times(91.5 - 48.2)}\)
\(=\sqrt{91.5\times22.1\times26.1\times43.3}\)
\(=\sqrt{91.5\times22.1\times(26.1\times43.3)}\)
\(=\sqrt{91.5\times22.1\times1130.13}\)
\(=\sqrt{(91.5\times22.1)\times1130.13}\)
\(=\sqrt{2024.15\times1130.13}\)
\(\approx\sqrt{2287397.54}\approx1511.72\)

Answer:

1511.72