The base of a pyramid is a right triangle with the longest side = 12cm. All non base edges are also equal to 12cm. And how can I find the height of the pyramid?

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Corinne Choi · Accepted Answer

Use Thales&#039; theorem.You can select the points  A  =  (  −  6  ,  0  ,  0  )  ,  B  =  (  +  6  ,  0  ,  0  )  ,to form the longest side of the base triangle. The other point   C lies on a circle of which   A  B is the diameter, as      y    2    +        [    6  −  x                ]        2    +      y    2    +        [    6  +  x                ]        2    =  144  ,so      x    2    +      y    2    =  36The top point   T is given by   (  0  ,  0  ,  z  ) and it is clear that  |  A  T  |  =  |  B  T  |  =  |  C  T  |as   A,   B and   C lie on the same circle, as   |  A  T  |  =  |  B  T  |  =  |  A  B  |, we obtain  z  =  6      3

The base of a pyramid is a right triangle with

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