Question

I need help with the work question 8Area of Regular PolygonsFind the area of each regular polygon. Leave your answer in simplest form. Ok

Answer 1

The area os any regular polygon is given by:

`A=(1)/(2)Pa`

where P is the perimeter and a is the apothem. The perimeter of a regular polygon is given by:

`P=ns`

where n is the number of sides and s is the length of its side. In this case we have a triangle, then n=3; we also know the length of the side, plugging these values we have:

`\begin{gathered} P=(3)(28√(3)) \\ P=84√(3) \end{gathered}`

Plugging the value of the perimeter and the apothem on the expression for the area we have:

`\begin{gathered} A=(1)/(2)(84√(3))(14) \\ A=588√(3) \end{gathered}`

Therefore, the area of the triangle is:

`A=588√(3)`

This is approximately 1018.4 square units