Question

Find the area of a triangle whose sides are $a=2,b=2,c=2.$

Short answer

Required area of the triangle is$1.73squareunits$

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

$$\begin{gathered} Given, \\ a=2,b=2,c=2 \\ Then, \\ s=\raisebox{1ex}{$a+b+c$}\!\left/ \!\raisebox{-1ex}{$2$}\right. \\ =\raisebox{1ex}{$2+2+2$}\!\left/ \!\raisebox{-1ex}{$2$}\right. \\ =\raisebox{1ex}{$6$}\!\left/ \!\raisebox{-1ex}{$2$}\right. \\ =3 \\ Now,Heron\text{'}sformulagivesareaas \\ Area=\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)} \\ =\sqrt{3\left(3-2\right)\left(3-2\right)\left(3-2\right)} \\ =\sqrt{3\times 1\times 1\times 1} \\ =\sqrt{3}=1.73squareunits \end{gathered}$$