Question

19.Use Heron's Formula, that is, the area of a triangle is A= s(-a)(6-b)(8-c), where thetriangle contains sides a, b and c and s=5(a+b+c) to find the area of the triangle with side1lengths: a = 12.4, b = 13.7, c = 20.2.84.9 square units138.4 square units125.2 square units83.3 square units

Answer 1

As indicated in the instructions we use Heron' s formula, for that we first calculate the semiperimeter of the triangle:

`s=(1)/(2)(12.4+13.7+20.2)=23.15\text{ untis}`

Now, we substitute this into Heron's formula:

`\begin{gathered} A=\sqrt[]{s(s-a)(s-b)(s-c)}=\sqrt[]{23.15(23.15-12.4)(23.15-13.7)(23.15-20.2)} \\ =\sqrt[]{6937.66}=83.3squareunits \end{gathered}`