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Sat 9 Oct, 2004 12:52 pm
Picture this:
A triangular pyramid made up of 4 equilateral triangles all of side = s.
A square pyramid made up of 4 equilateral triangles all of side = s, and a square base.
Now take the two pyramids and place them together so that a triangular face of one matches a triangular face of the other.
How many faces does the resulting figure have?
I get seven.
The square pyramid has five faces. The triangular has four. Putting them together along one triangular face cancels out two faces.
There would be six if the triangular base and the square base ended up in the same plane.
The way I see it two are chancelled out and two join together in one face with a parallellogram shape.
Whim
I must agree with merlinsgodson the two bases would not be on the same plane.
I get seven as well.
This is a trickier problem than first seems at first.
It was a question on an SAT exam, and the standard answer was number of faces = 5+4-2 = 7
However one student who had a wonderful ability to visualize spacial figures, saw that not only would 2 faces get lost due to facing each other, but also that 2 other pairs of faces would be coplanar.
He gave an answer of 5 (!!) , which was obviously marked incorrect.
Somehow, he found out that his answer was marked wrong and he contested it ... successfully.
I myself had to construct the figures to convince of the answer.
Ok, that what I thought too, still I must have gone wrong with the counting. I counted six faces.
I will have to make me a model like you did.
Whim
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