A polyhedron has 7 faces and 15 edges. How many vertices does this polyhedron have?

Open in App

Solution

Dear Student,

$A c c o r d i n g t o E u l e r' s T h e o r e m, i n a n y s o l i d s h a p e, F a c e s + V e r t i c e s - E d g e s = 2 \Rightarrow 7 + V e r t i c e s - 15 = 2 \Rightarrow V e r t i c e s = 10 T h u s, t h e p o l y h e d r o n h a s 10 v e r t i c e s .$

Suggest Corrections

Similar questions

Can a polyhedron have 7 faces, 10 vertices and 15 edges?

If a polyhedron has 15 vertices and 20 edges, then it has ___ faces.

Join BYJU'S Learning Program