SOLUTION: Good day! Can you please help me solve this problem?
Find the length of a diagonal of a regular octahedron if its edges measure 5 cm.
Thank you very much!
Question 1001900: Good day! Can you please help me solve this problem?
Find the length of a diagonal of a regular octahedron if its edges measure 5 cm.
Thank you very much! Answer by ikleyn(52780) (Show Source): You can put this solution on YOUR website! .
Find the length of a diagonal of a regular octahedron if its edges measure 5 cm.
--------------------------------------------------------------------
A regular octahedron with the edge measure 5 cm is shown in the Figure below.
Figure. A regular octahedron
It has 8 faces, each of which is a regular triangle. All edges of a regular octahedron are congruent
(have the same measure).
You can imagine a regular octahedron as comprised of two rectangular pyramids whose two square bases are joined
and overposed each to the other.
Notice that the horizontal section of a octahedron (as it is shown in the Figure) is a square.
The vertical section of a octahetron is a square too. These squares are congruent and have the same side measures.
A diagonal of octahedron is a diagonal of one of these two square.
Thus octahedron has 4 diagonals, and these diagonals have the same measure.
So, this measure is , where a is the measure of the octahedron edge.
In your case the measure of the octahedron diagonals is cm.