Question
The perimeter of a regular hexagonal pyramid is 24 cm. The angle between the pyramid's slant height and hexagon's apothem is 60 degrees. find the volume of the pyramid
Answers
Each side of the base is 6 cm ------- (24/6)
make a sketch of the hexagon base to find its apothem, the distance
from the centre to the midpoint of a side.
Consider one of the equilateral triangles of side 6
You should have no difficulty to find the apothem to be 3√3
you said the angle between slant and apothem is 60°
let the height of the pyramid be h cm
then tan60° = h/3√3
h = 3√3tan60 = 9
volume = (1/3)(base)(height) = (1/3)(base)(9) = 3base
I will leave it up to you to find the area of the hexagon
make a sketch of the hexagon base to find its apothem, the distance
from the centre to the midpoint of a side.
Consider one of the equilateral triangles of side 6
You should have no difficulty to find the apothem to be 3√3
you said the angle between slant and apothem is 60°
let the height of the pyramid be h cm
then tan60° = h/3√3
h = 3√3tan60 = 9
volume = (1/3)(base)(height) = (1/3)(base)(9) = 3base
I will leave it up to you to find the area of the hexagon