Question

Find the area of regular polygon. can anyone help me been stuck with this for hours

Answer 1

Answer:

Step-by-step explanation:

Area of hexagon given apothem. (The line that is 5 rad 3)

The apothem is perpendicular to the side of the hexagon, forming a triangle with the corner of the hexagon. The angle measurement of the corner is 60 degrees because the angle measurement of any interior angle of a regular hexagon is 120. this means that the imaginary triangle connecting the apothem to the closest corner and that to the center is a 30-60-90 triangle.

The sides of a 30-60-90 triangle are

a (the shortest side)= x

b (The longer leg/ apothem in this scenario)= x rad 3

c (hypotenuse)=2x

a=5

b=5 rad 3

c=10

2a= side length = 10

using the formula for hexagon area

A =((3 rad 3)/2) s^2

where s is the side

(3 rad 3)/2 x 100

A=259.81

Answer 2

Answer:

The answer to your question is 259.8 cm²

Step-by-step explanation:

Formula

             Area = $\frac{Perimeter x A}{2}$

See the picture below

1.- Find the perimeter

From the right triangle find the lenght of one side

    tan 30° = $\frac{x}{5\sqrt{3} }$

    x = $5\sqrt{3} tan30°$

    tan 30° = $\frac{1}{\sqrt{3} }$

Then

   x = $5\frac{\sqrt{3} }{\sqrt{3} }$

   x = 5

  lenght of a side = 2x = 2(5) = 10

Perimeter = 10 x 6

                = 60

2.- Find the area

           $Area = \frac{60 x 5\sqrt{3} }{2}$

           $Area = 30x5\sqrt{3}$

           $Area = 150\sqrt{3}$

          $Area = 259.8 cm^{2}$