perplexus.info :: Shapes : Pyramid from a square

Pyramid from a square (Posted on 2021-07-29)

Take a unit square of paper ABCD. Label the midpoints of BC and CD by E and F. Fold up along AE, EF, and AF so that B, C, and D come together and a tetrahedral pyramid is formed.

Find the height to the base AEF.

https://www.desmos.com/calculator/mh2ibfjuth

Submitted by Jer

Rating: 4.0000 (1 votes)

Solution: (Hide)

Any of the four sides of the pyramid can be the base. Let's make ECF the base so the height is the perpendicular AD.
Area [ECF]=1/8, Height AD=1 so volume is Bh/3=(1/8)(1)/3 = 1/24 cubic unit.
Turning back to base AEF, we have a triangle that looks complicated but it actually the square minus the three right triangles.
[ABCD] - [ABE] - [ECF] - [FDA] = [AEF]
1 - 1/4 - 1/8 - 1/4 = 3/8
Using the volume formula again
V=Bh/3
(1/24)=(3/8)h/3
h=1/3

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
No Subject	Metalin	2021-08-30 01:18:45
re: solution	Jer	2021-08-07 11:30:27
solution	Charlie	2021-07-29 11:32:35

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