This is kind of urgent because i got a deadline soon and it would be nice if i could get help as soon as possible.
Regular hexagon ABCDEF is the base of right pyramid PABCDEF. If PAD is an equilateral triangle with side length 8, then what is the volume of the pyramid?
If we inscribed the hexagonal bsse in a circle, AD would be a diameter of 8 and the radius of this circle = side of the hexagon = half of this = 4 units
The height of the pryramid can be found as
sqrt (8^2 - 4^2) = sqrt (64 - 16) = sqrt (48) = 4sqrt (3)
The area of the base is just the area of the hexagon = area of 6 equilateral triangles with sides of 4
So the base area =
6(1/2) (4)^2 sqrt (3) / 2 =
24sqrt (3) units ^2
So...the volume of the pyramid =
(1/3) base area * height =
(1/3) (24 sqrt (3) ) * (4 sqrt (3)) =
(1/3) (96) (3) =