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The area scale factor in such a situation is the square of the length scale factor.
http://www.mathsisfun.com/geometry/tria … orems.html
Thanks,is there any proof without calculus,i'm just curious.
where H is the height of the pyramid.
Because the dark blue base region is mathematically similar to the light blue region the areas, small:large, will be in this proportion:
Now for a little integral calculus:
Imagine the solid divided into thin slices parallel to the base with thickness delta x.
So let the slices become infinitesimally thin with thickness 'dx', and sum all slices from the top to the base
Furthermore, the pyramid need not be 'right', ie. the axis at right angles to the base. If a right pyramid is sheared parallel to the base, so that it leans over, the slices still have the same area, so the volume formula continues to work, provided H is the perpendicular height. (picture in next post)
He actually wants to ask about a general formula for a pyramid
A isoceles triangle base pyramid's apex is on top of the triangle's top vertex,what is it's volume?is there a formula?how was it derived?