Answer :

stavyk012

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

joseaaronlara

Answer:

The answer to your question is 259.8 cm²

Step-by-step explanation:

Formula

             Area = [tex]\frac{Perimeter x A}{2}[/tex]

See the picture below

1.- Find the perimeter

From the right triangle find the lenght of one side

    tan 30° = [tex]\frac{x}{5\sqrt{3} }[/tex]

    x = [tex]5\sqrt{3} tan30°[/tex]

    tan 30° = [tex]\frac{1}{\sqrt{3} }[/tex]

Then

   x = [tex]5\frac{\sqrt{3} }{\sqrt{3} }[/tex]

   x = 5

  lenght of a side = 2x = 2(5) = 10

Perimeter = 10 x 6

                = 60

2.- Find the area

           [tex]Area = \frac{60 x 5\sqrt{3} }{2}[/tex]

           [tex]Area = 30x5\sqrt{3}[/tex]

           [tex]Area = 150\sqrt{3}[/tex]

          [tex]Area = 259.8 cm^{2}[/tex]    

${teks-lihat-gambar} joseaaronlara

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