ISEE Upper Level Math : How to find the volume of a tetrahedron
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Example Question #4 :Tetrahedrons
In three-dimensional space, the four vertices of a tetrahedron - a solid with four faces - have Cartesian coordinates
Give its volume.
四面体是一个三棱锥,可以looked at as such.
Three of the vertices -
Its base and height are both 18, so its area is
The fourth vertex is off the
Example Question #1 :Tetrahedrons
In three-dimensional space, the four vertices of a tetrahedron - a solid with four faces - have Cartesian coordinates
Give its volume in terms of
四面体是一个三棱锥,可以looked at as such.
Three of the vertices -
Its base is 12 and its height is 15, so its area is
The fourth vertex is off this plane; its perpendicular (vertical) distance to the aforementioned face is the difference between the
Example Question #61 :Solid Geometry
In three-dimensional space, the four vertices of a tetrahedron - a solid with four faces - have Cartesian coordinates
Give its volume in terms of
The correct answer is not among the other choices.
四面体是一个三棱锥,可以looked at as such.
Three of the vertices -
Its base is 20 and its height is 9, so its area is
The fourth vertex is off this plane; its perpendicular (vertical) distance to the aforementioned face is the difference between the
Example Question #7 :Tetrahedrons
In three-dimensional space, the four vertices of a tetrahedron - a solid with four faces - have Cartesian coordinates
What is the volume of this tetrahedron?
The tetrahedron looks like this:
This is a triangular pyramid, so look at
The volume of the tetrahedron, it being essentially a pyramid, is one third the product of its base and its height, the latter of which is 12. Therefore,
Example Question #8 :Tetrahedrons
Above is the base of a triangular pyramid, which is equilateral.
Altitude
By the 30-60-90 Theorem,
The area of the triangular base is half the product of its base and its height:
The volume of the pyramid is one third the product of this area and the height of the pyramid:
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