Find the area of a regular hexagon if each side is 8cm long.(leave the answer in radical form).

Answer 1

Area = (3sqr3/2)s^2 = a 3sqr3/2 x 6^2 = 3sqr3/2 x 36

= 18 x 3sqr3 = 54sqr3 = about 54(1.732) = 93.531 cm^2

a hexagon has (n-2)180 = (6-2)180 = 4(180) = 720 degrees total interior angles. each interior angle = 720/6 = 120 degrees. Use that to create 4 right triangles and a rectangle in the middle

divide the hexagon into 5 parts, a rectangle in the middle which is 6 by 6sqr3 with area = 36sqr3

and 4 triangles each 3 by 3sqr3

each triangle has area 9sqr3/2

4 times that = 18sqr3

add 18sqr3 + 36sqr3 = 54sqr3 = area of the hexagon