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Suppose PABCD is a right square pyramid with apex P and base ABCD. If PBD is an equilateral triangle with side length 6, then what is the volume of PABCD?

 Nov 25, 2019
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BD  is a diagonal  of the base....so.....since the base is square.....one side of the base = 6/√2

 

The height of the equilatreal triangle  =  height of the pyramid .....so....

 

tan 60°  =  height of pyramid / 3

 

3 tan 60°  =  height of pyramid

 

3√3  = height of pyramid

 

So....the volume of the pyramid  = 

 

(1/3)  base area *  height  =

 

(1/3) (6/√2)^2 * 3√3  =

 

18√3   units^3

 

 

cool cool cool

 Nov 26, 2019

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