HOW TO FIND AREA OF REGULAR HEXAGON

Find the perimeter area of each regular polygon. Leave your answer in simplest form.

Example 1 :

Solution :

Number of sides = 6

Perimeter of the shape = 6 x 10

= 60 cm

Perimeter = 60 cm

Length of apothem = 5√3 cm

Example 2 :

Solution :

Number of sides of a polygon = 6

by drawing lines from center to each vertex, we may draw six triangles of equal measure.

Angle measure of each triangle = 360/6 ==> 60

In triangle OAB,

OB = Hypotenuse, smaller side = AB

OB = 2(AB)

In special right triangle, the side which is opposite to 60 is √3(Smaller side).

OA = 4√3 then AB = 4 and OB = 2(4) ==> 8

Side length = 2(4) ==> 8

Example 3 :

Solution :

Central angle of one triangle = 360/60

= 60 degree

OB = 8, AB = Smaller side

2AB = OB, then AB = 4

OA = 4√3 (Apothem)

Side length = 8

Perimeter = 6(8) ==> 48

Area = (1/2) x 48 x 4√3

= 24 x 4√3

= 96√3 square units.