Question

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

Answer 1

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

The answer to your question is 259.8 cm²

Explanation:

Formula

Area =
`(Perimeter x A)/(2)`

See the picture below

1.- Find the perimeter

From the right triangle find the lenght of one side

tan 30° =
`(x)/(5√(3) )`

x =
`5√(3) tan30°`

tan 30° =
`(1)/(√(3) )`

Then

x =
`5(√(3) )/(√(3) )`

x = 5

lenght of a side = 2x = 2(5) = 10

Perimeter = 10 x 6

= 60

2.- Find the area

`Area = (60 x 5√(3) )/(2)`

`Area = 30x5√(3)`

`Area = 150√(3)`

`Area = 259.8 cm^(2)`