Question

Find the area of the polygon. (hint: you need to solve for missing apothem or sides).Also round the area to the nearest whole number

Answer 1

The hexagon given is a regular hexagon. With apothem of 15 in

Area of a hexagon =

`\begin{gathered} =(1)/(2)* a* P \\ \text{where a = apothem} \\ p=\text{perimeter of the hexagon} \end{gathered}`

Let us calculate the perimeter of the hexagon

From the triangle above,

`\begin{gathered} \text{tan 60=}(15)/(x) \\ x\text{ tan 60 = 15} \\ x=(15)/(\tan 60) \\ x=5\sqrt[]{3} \end{gathered}`
`\text{The side length of the hexagon = 2x = 2(5}\sqrt[]{3})\text{ = 10}\sqrt[]{3}\text{ in}`
`\text{The perimeter of the hexagon = 6 x 10}\sqrt[]{3}\text{ = 60}\sqrt[]{3}\text{ in}`
`\begin{gathered} \text{Area of the hexagon = }(1)/(2)* a* P \\ =(1)/(2)\text{ x 15 x 60}\sqrt[]{3} \\ =779.42in^2 \\ \\ Hence,\text{ the area of the polygon is }779in^2\text{ (to nearest wholw number)} \end{gathered}`