SOLUTION: For a ballet production, a truncated pyramid is constructed with a square base of 10 meters on a side, a height of 8 meters and a summit height of 2 meters. What is the total area

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Question 1207323: For a ballet production, a truncated pyramid is constructed with a square base of 10 meters on a side, a height of 8 meters and a summit height of 2 meters. What is the total area of the surfaces of the truncated pyramid?
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13334) About Me  (Show Source):
You can put this solution on YOUR website!


The problem as stated is nonsense, since we don't know what "summit height" of 2 meters is.

It is a good problem if we assume that the 2 meters is supposed to be the length of a side of the square top of the truncated pyramid. So I'll go ahead with that assumption.

Consider the pyramid before it was truncated.

Use similar triangles and the given dimensions to determine that the height of the original pyramid was 10m.

The slant height of a face of the original pyramid (peak to midpoint of a side of the base) is the hypotenuse of a right triangle with legs 5m and 10m:

h=sqrt%285%5E2%2B10%5E2%29=sqrt%28125%29=5sqrt%285%29

The area of each triangular face of the original pyramid is (one-half base times height)

A=%281%2F2%29%2810%29%285sqrt%285%29%29=25sqrt%285%29

The area of each face of the small pyramid that was cut off to form the truncated pyramid is

A%2B%281%2F2%29%282%29%28sqrt%285%29%29=sqrt%285%29

So the area of each face of the truncated pyramid is

25sqrt%285%29-sqrt%285%29=24sqrt%285%29

The total surface area of the truncated pyramid is the area of the two bases, plus the area of the four faces:

%28100%2B4%29%2B4%2824sqrt%285%29%29=104%2B96sqrt%285%29

ANSWER: 104%2B96sqrt%285%29 square meters

Answer by ikleyn(53763) About Me  (Show Source):
You can put this solution on YOUR website!
.

The term  " a summit height "  is  NEVER  used in  Math and is  NEVER  used in geometry.

This combination of words is  UNDEFINED  term,  and its meaning in this problem
is as dark as midnight in a forest,  at no moon.


To a person who created this mess,  I'd like to remind that Math is a system of knowledge,
expressed in certain terms of its language,  but not a warehouse of words to combine them in an arbitrary way.