Question

Find the area of a triangle whose sides are $a=4,b=3,c=6.$

Short answer

Required area of the triangle is$5.33squareunits.$

Step-by-step solution

Step 1. Given information 

The area of a triangle with sides a, b, and c is determined by the Heron's formula which is given as:

$$\begin{gathered} Area=\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)} \\ where, \\ s=\raisebox{1ex}{$a+b+c$}\!\left/ \!\raisebox{-1ex}{$2$}\right. \end{gathered}$$

Step 2. Calculation

$$\begin{gathered} Given, \\ a=4,b=3,c=6 \\ then, \\ s=\raisebox{1ex}{$a+b+c$}\!\left/ \!\raisebox{-1ex}{$2$}\right. \\ =\raisebox{1ex}{$4+3+6$}\!\left/ \!\raisebox{-1ex}{$2$}\right. \\ =\raisebox{1ex}{$13$}\!\left/ \!\raisebox{-1ex}{$2$}\right. \\ =6.5 \\ now,Heron\text{'}sformulagivesareaas \\ Area=\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)} \\ =\sqrt{6.5\left(6.5-4\right)\left(6.5-3\right)\left(6.5-6\right)} \\ =\sqrt{6.5\times 2.5\times 3.5\times 0.5} \\ =\sqrt{28.4375} \\ =5.3326\approx 5.33squareunits. \end{gathered}$$