Question

A) What is the perimeter of the regular hexagon show. in the picture?B) What is the area of the regular hexagon shown in the picture?(see attached image)

Answer 1

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

`\begin{gathered} U\sin g\text{ pythagoras theorem } \\ \text{Hyp}^2=opp^2+adj^2\text{ } \\ 12^2\text{ = }x^2\text{ + (}(x)/(2))^2 \\ 144=x^2+(x^2)/(4)^{} \\ 144\text{ = }(4x^2+x^2)/(4) \end{gathered}`
`\begin{gathered} 144\text{ = }(5x^2)/(4) \\ \text{cross multiply } \\ 144(4)=5x^2 \\ 576=5x^2 \\ \text{divide both side by 5} \\ x^2\text{ = }(576)/(5) \\ x^2\text{ = 115.2} \\ x\text{ = 10.7} \end{gathered}`

Step 3: Find the Perimeter of the hexagon

`\begin{gathered} \text{Perimeter = 6x} \\ \text{Perimeter = 6(10.7)} \\ \text{Perimeter = 64.4} \end{gathered}`

Step 4: Find the Area of the hexagon

`\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}`

Hence the perimeter and area of the hexagon are 64.4 and 27.89