Question

How would you find the perimeter of a regular polygon with this information provided?

Answer 1

Given that the polygon is regular, it implies that the interior angles and the sides are equal.

If the length of the sides are equal, then we can conclude that;

`\begin{gathered} 5(x+2)=7x+4 \\ \end{gathered}`

By solving the above equation, we can get the value of x

`\begin{gathered} 5(x+2)=7x+4 \\ 5x+10=7x+4 \\ 5x-7x=4-10 \\ -2x=-6 \end{gathered}`

Divided both side by -2 to get x

`\begin{gathered} (-2x)/(-2)=(-6)/(-2) \\ x=3 \end{gathered}`

Since the value of x is 3, the length of one side of the hexagon can be obtained by substituting x=3 in 5(x+2)

`\begin{gathered} x=3 \\ 5(x+2)\Rightarrow5(3+2)\Rightarrow5(5)\Rightarrow25\text{units} \end{gathered}`

The hexagon has side of length 25units and the image is shown below

The perimeter of the polygon( hexagon) is given as the sum of the outline and this is given below

`\text{Perimeter}\Rightarrow25+25+25+25+25+25=150units`

Hence, the perimeter of the regular polygon is 150 units