# Thread: volume of a triangular wedge

1. suppose we have a triangular prism ABC DEF[=A'B'C'], base: isosceles rectangle ABC [angle 90° at B]of side a=a and height h : volume is a²*h / 2
suppose now we cut it with a plane passing through B and DF , do you know the formula to calculate the volume of the [one of the] two solids?
Thanks  2.

3. Is this homework?  4. I wish it were, Harold, my grandson left school!, a link will do.  5. If I have pictured it correctly, one of the shapes is a pyramid with triangular base DEF and height h. Base DEF is the same as ABC, that is, it is a right triangle with two equal sides of length a. The area of the base is a² / 2.
Pyramid (geometry) - Wikipedia, the free encyclopedia says the volume of a pyramid is Bh/3 where B is the area of the base and h is the height from the base to the apex.
This gives us V=a² h/ 6.  6. let's start with the cuboid ABCD, A'B'C'D', with square base a², V=a²h, we cut it diagonally and we get a triangular prism with triangular base ABC : V= a²h/2, now we cut it in two pieces with a plane passing trough B' and AC, the volume of this pyramid-wedge is one third and the other pyramid-pyramid with base AA'BB' 2/3 V =a²h/3. Is that right?, so the cuboid V divides into 3 pyramid-parts, one of these is divided into two wedges. thanks Harold  7. The area of the other piece of the prism is a² h/ 2- a² h/ 6 = a² h/ 3, so I agree. What is the point of all this, Ray?  8. don't be suspicious again, I thought Volume of a pyramid is different when vertex is not central  9. I'm not suspicious, Ray. Just wondering why you posted this geometry problem.  10. Originally Posted by ray , I thought Volume of a pyramid is different when vertex is not central
just so, sorry if I disturbed you  Bookmarks
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