find volume......

Question

Given: ABCD pyramid All edges congruent AB = 4.5 Find: V

Answer 1

Hi,

I think this is a triangular pyramid. Given that all edges are equal, all faces are equilateral triangles and it is a regular tetrahedron. The volume of a regular tetrahedron is

V = a^3/6 sqrt 2

where a is the side. Substitute a = 4.5 above and you can find the volume.

Hope this helps!

Answer 2

Hi Dan C.,

So it's a square pyramid. You know how to find the base area, right? (4.5*4.5=?). Now for the height, and the formula from there.

Height is established via the Pythagorean Theorem, from triangles using the base and the vertical to the apex.

Your first triangle is ON the base, defined by one base edge and portions of the intersecting diagonals between the vertices of the base. Since the hyponenuse of that triangle is the edge length (4.5), and it is a 45-45-90 triangle, the leg from a vertex to the center of the base has length: ? (I recommend keeping the root, and calculating at the end, if your course allows/requires that).

So now you have a second right triangle. Use the segment whose length you just obtained as one leg, the height of the pyramid as the second leg, and the edge between the loose ends as the hypotenuse. Solve for the height.

You now have the base and the height.

As you may know from calculus, if you summate a series consisting of squares (both geometrically, as slices, and mathematically, as a series) you have performed an integration, to obtain (1/3)d^3. The d^3 is irrelevant here (since your height and edge are not identical), but the (1/3) factor is highly relevant: it is the coefficient in the equation for a pyramid

V = (1/3)bh . (Also for a cone, a triangular pyramid, a pentagonal pyramid .....). I'll leave the calculation from there on for you.

-- Cheers, --Mr. d.