Question
I need help finding the area of a regular hexagon with an apothem of 6cm. No side length is given
Answers
mathhelper
The apothem is the perpendicular distance to the base, and you know that
all angles are 60°
You should the ratio of sides of the standard 30-60-90 triangle, you can see
such a triangle.
by simple ratios the base of such a triangle with height of 6 cm is 2√3
so each side of the hexagon is 4√3
area of one of the six triangles = (1/2)(4√3)(6) cm^2
= 12√3 cm^2
and since we have 6 of those .......
You could also find the side of the hexagon this way:
let each side be 2x,
then tan60° = 6/x
x = 6/tan60 = 6/√3
= 6/√3 * √3/√3
= 2√3
so each side is 2x = 4√3, just as before
all angles are 60°
You should the ratio of sides of the standard 30-60-90 triangle, you can see
such a triangle.
by simple ratios the base of such a triangle with height of 6 cm is 2√3
so each side of the hexagon is 4√3
area of one of the six triangles = (1/2)(4√3)(6) cm^2
= 12√3 cm^2
and since we have 6 of those .......
You could also find the side of the hexagon this way:
let each side be 2x,
then tan60° = 6/x
x = 6/tan60 = 6/√3
= 6/√3 * √3/√3
= 2√3
so each side is 2x = 4√3, just as before
eoptify on yt
tysm