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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?**

Thanks!

Guest Mar 6, 2019

#1**+2 **

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) =

96 units^3

CPhill Mar 6, 2019