Thread: Regular pyramid

Hi!
Yesterday we had a exercise in geometry, it was said:
A regular triangle pyramid with all of its edges 5cm long. There is a smaller triangle that is cutting the edge in half. Need to calculate volume and full surface area.
Here is a small picture of the figure -


As far as I could figure out this one, the bigger triangle is 2 times bigger then the smaller one, area is 2^2 times bigger.

Originally Posted by regdude

Hi!
Yesterday we had a exercise in geometry, it was said:
A regular triangle pyramid with all of its edges 5cm long. There is a smaller triangle that is cutting the edge in half. Need to calculate volume and full surface area.
Here is a small picture of the figure -


As far as I could figure out this one, the bigger triangle is 2 times bigger then the smaller one, area is 2^2 times bigger.

correct, and the volume of the larger would be times as large.

here is a link to all kinds of good info re: tetrahedrons ...

Tetrahedron -- from Wolfram MathWorld

The weirdest thing about this exercise is one of its answer - 21.875*sqrt(3) (I think, but something like that).
Tried to mark one of the triangles edge as "x" to see if somewhere I can get an equation that would cancel out those "x".
Only equation that I saw to have division was this:
H1^2 / H2^2 = S1 / S2
height squares are proportional to triangle areas.
Another way to get rid of "x" is to have right triangles and use this simple equation: b^2 = a^2 - c^2
But couldn't find any right triangle that would give me a^2 on both sides.