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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!

 Mar 6, 2019
 #1
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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

 

cool  cool cool

 Mar 6, 2019
 #2
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Thank you!

Guest Mar 6, 2019

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