Step 1: Figure of a regular hexagon shown below
Step 1: Determine the length of the side of the hexagon
Let the side of the hexagon = x
[tex]\begin{gathered} U\sin g\text{ pythagoras theorem } \\ \text{Hyp}^2=opp^2+adj^2\text{ } \\ 12^2\text{ = }x^2\text{ + (}\frac{x}{2})^2 \\ 144=x^2+\frac{x^2}{4}^{} \\ 144\text{ = }\frac{4x^2+x^2}{4} \end{gathered}[/tex][tex]\begin{gathered} 144\text{ = }\frac{5x^2}{4} \\ \text{cross multiply } \\ 144(4)=5x^2 \\ 576=5x^2 \\ \text{divide both side by 5} \\ x^2\text{ = }\frac{576}{5} \\ x^2\text{ = 115.2} \\ x\text{ = 10.7} \end{gathered}[/tex]
Step 3: Find the Perimeter of the hexagon
[tex]\begin{gathered} \text{Perimeter = 6x} \\ \text{Perimeter = 6(10.7)} \\ \text{Perimeter = 64.4} \end{gathered}[/tex]
Step 4: Find the Area of the hexagon
[tex]\begin{gathered} A=3\frac{\sqrt[\square]{3}}{2}a \\ A\text{ = 3}\frac{\sqrt[\square]{3}}{2}\text{ (10.7)} \\ \text{A = 27.89} \end{gathered}[/tex]
Hence the perimeter and area of the hexagon are 64.4 and 27.89
