Question

A polyhedron has 7 faces and 10 vertices. How many edges does it have

Answer 1

`EULER'S \: \: \: FORMULA \: - \\ \\ \\ For \: any \: convex \: polyhedron \: , \: the \: \\ number \: of \: vertices \: and \: faces \: \\ together \: is \: exactly \: two \: more \: than \\ \: the \: number \: of \: edges. \: \\ \\ Symbolically \: , \\ V-E+F=2 \\ \\ Here \: , \: F=7 \: \: and \: \: V=10 \\ \\ We've \: \: to \: \: find \: \: E \\ Using \: \: Euler's \: \: Formula \: \: , \\ \\ 10 - E + 7 = 2 \\ \\ \\ E \: = \: 15 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: Ans.`