Quandaries and Queries



How do I calculate the volume of an irregular shaped tetrahedron where:-
side a = 1.4 m
side b = 1.4 m
side c = 1.2 m
and height = 0.75 m at the junction of sides a and b.

Thank you in anticipation




Hi Peter,

The volume follows from a result that says if you take some region R in the plane with an area, some point P not in the plane and form a cone by joining every point on the boundary of R to P with a straight line then the volume of the cone is 

1/3  (the area of the base)  (the height).

By your description you have a tetrahedron with a base triangle having sides of lengths a, b and c and a vertex P which is 0.75 m above the plane containing the base triangle.

The volume of the tetrahedron is then

1/3  (the area of the base triangle)  0.75 m3

The area of the base triangle can be found using Heron's Formula.



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