Question

Suppose one takes a tetrahedron $ABCD$ with base $ACD$ as shown and combines it with another tetrahedron by connecting their corresponding bases. How many distinct edges does the resulting object have?

• A. $9$
• B. $12$
• C. $10$
• D. $11$
• E. $8$

Answer 1

The correct option is A $9$

Solution:

After joining two tetrahedron by connecting their bases.

We have,

Number of vertices $V=5$

Number of faces $F=6$

Number of Edges $=?$

By Euler's Polyhedral Formula

$V+F-E=2$

or, $5+6-E=2$

or, $E=11-2=9$

So, Number of Edges $=9$

Hence, A is the correct option.