Question

A solid has two bases and 5 lateral faces. What is the sum of the number of vertices and edges combined?

Answer 1

Answer:

25

Step-by-step explanation:

we know that

If the solid has two bases and 5 lateral faces, then the number of vertices is equal to 5 in each base

so

$Vertices=2(5)=10$

The number of edges is equal to 5 in each base plus 5 edges of the lateral faces

so

$Edges=2(5)+5=15$

therefore

The number of vertices and edges combined is equal to

$Vertices+Edges=10+15=25$

Verify

we know that

Euler’s formula for any polyhedron is given by the formula

$F+V-E=2$

where

F is the number of faces

V is the number of vertices

E is the number of edges

we have

$F=2+5=7$ ---> 2 bases and 5 lateral faces

$V=10\\E=15$

substitute

$7+10-15=2$ ----> is ok