Question

How far from the base of a pyramid of altitude 10 m is a section parallel to the base and equal in area to half of the base?

Answer 1

its asking you to work how how far vertically from the point can you cut the top off, and have the base of the new tiny pyramid that has half the area of the base of the full pyramid

Answer 2

so whats the relationship between altitude and area @cassie93 ?

Answer 3

are u there...?

Answer 4

i don't get it..

Answer 5

think about how the side length of the pyramid varies with the height
then think about how the area of the section parallel to the base varies with the side length

Answer 6

...look at a section halfway down the pyramid. What fraction of the area of the base does the section parallel to the base halfway down the pyramid have?

Answer 7

1/2 ?

Answer 8

not quite, the length of the side halfway down the pyramid is half the length of the side at the bottom, so the section halfway down will have 1/4 of the area. Do you want me to try to draw this?

Answer 9

yup..plz..

Answer 10

the bigger rectangle is the base, the smaller rectangle is a slice about halfway up the pyramid

Answer 11

each side of the slice is about half as long as the side of the bigger rectangle. how does the area of the smaller rectangle compare to the area of the bigger rectangle?

Answer 12

1/4..? but there's no dimension..

Answer 13

sorry, I didn't explain that very well. Start over.

Answer 14

As the height changes, how does the length of the side of the section change?

Answer 15

i don't know.. whts the relationship? is it by using Pythagoras theorem?

Answer 16

sorry, I was writing a college application essay.
no, it's not using the pythagorean theorem, it's linear.

you can use similar triangles to find the length of the side of the slice in terms of (something)

Answer 17

this is all getting kinda complex, is it 1/ sqrt 2?
so 0.707 x 10 = 7.07 = ht (for a square based pyramid) ... yeah?

Answer 18

yes, jack, you're right.