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A pyramid is formed on a 6x8 rectangular base. The four edges joining the apex to the corners of the rectangular base each have length 13. What is the volume of the pyramid?

 Jan 13, 2019

Best Answer 

 #1
avatar+18346 
+3

Need to find h    the height of the pyramid....then volume = lwh/3

 

the diagonal of the base (using Pythag Theorem)    sqrt(6^2 + 8^2)  = 10

    now the mid point of the diagonal  and h   form another right triangle with hypotenuse 13 (given)

        so use pythag theorem again to find h       h^2 + 5^2 = 13^2     yields  h = 12

 

Volume = lwh/3  = (6)(8)(12)/3 = 192 units^3

 Jan 13, 2019
edited by ElectricPavlov  Jan 13, 2019
 #1
avatar+18346 
+3
Best Answer

Need to find h    the height of the pyramid....then volume = lwh/3

 

the diagonal of the base (using Pythag Theorem)    sqrt(6^2 + 8^2)  = 10

    now the mid point of the diagonal  and h   form another right triangle with hypotenuse 13 (given)

        so use pythag theorem again to find h       h^2 + 5^2 = 13^2     yields  h = 12

 

Volume = lwh/3  = (6)(8)(12)/3 = 192 units^3

ElectricPavlov Jan 13, 2019
edited by ElectricPavlov  Jan 13, 2019
 #2
avatar+36 
+2

Thanks! smiley

Starz  Jan 13, 2019

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