6,667 views
21 votes
21 votes
How many diagonals can be drawn inside a 3d rectangular shape , (I'm not asking about finding the length of diagonal) just the possible no. of diagonals ? please help​

User Ngozi
by
2.3k points

2 Answers

27 votes
27 votes

Answer:

4 diagonals if we do not count the interior of faces of the object

16 if we count the interior of the faces of the object

Explanation:

The key word is inside

I assume that means there are no diagonals drawn on the surface of the 3d rectangular prism

There are 4 possible diagonals that can be drawn.

Each interior diagonal can be drawn from the top vertex to the bottom diagonally opposite vertex

Since there are 8 vertices in all and two vertices are connected by a diagonal, there are a total of 4 interior diagonals that can be drawn

If we were to consider the interior faces of the object, since there are 6 faces and 2 diagonals can be drawn on each face that would be an additional 12 diagonals

So I am a little confused here whether the question includes the interior face diagonals. You may wish to clarify

If you look at the attached picture, you will see that there are 2 diagonals. One of the diagonals is on the base of the object, that other is from top vertex to opposite bottom vertex

So if you include both surface and interior that would be 16, if you ignore the surface, that would be 4

How many diagonals can be drawn inside a 3d rectangular shape , (I'm not asking about-example-1
User Eric Miller
by
2.5k points
17 votes
17 votes
2 can be drawn inside a 3d
User SirSaleh
by
3.2k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.