Question

5 multiple choice 1 point
find the area of the triangle.
a = 20.8
b = 15.2
c = 13.8
104.84
113.84
107.84
6 multiple choice 1 point
find the area of the triangle.
a = 19.8
b = 18.4
c = 13.9
132.02
126.02
123.02

Explanation:

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

For the first triangle:
\(s=\frac{a + b + c}{2}=\frac{20.8+15.2 + 13.8}{2}=\frac{49.8}{2}=24.9\)
For the second triangle:
\(s=\frac{a + b + c}{2}=\frac{19.8+18.4 + 13.9}{2}=\frac{52.1}{2}=26.05\)

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

For the first triangle:
\(A=\sqrt{24.9(24.9-20.8)(24.9 - 15.2)(24.9-13.8)}\)
\(=\sqrt{24.9\times4.1\times9.7\times11.1}\)
\(=\sqrt{24.9\times4.1\times(9.7\times11.1)}\)
\(=\sqrt{24.9\times4.1\times107.67}\)
\(=\sqrt{24.9\times441.447}\)
\(=\sqrt{10992.0303}\approx104.84\)
For the second triangle:
\(A=\sqrt{26.05(26.05 - 19.8)(26.05-18.4)(26.05 - 13.9)}\)
\(=\sqrt{26.05\times6.25\times7.65\times12.15}\)
\(=\sqrt{26.05\times6.25\times(7.65\times12.15)}\)
\(=\sqrt{26.05\times6.25\times92.9475}\)
\(=\sqrt{26.05\times580.921875}\)
\(=\sqrt{15133.01584}\approx123.02\)

Answer:

1. \(104.84\)
2. \(123.02\)