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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

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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
0

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
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Thanks! Starz  Jan 13, 2019