Question

I.
2. Verify Euler's formula for the following solids.
b.
a.
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Joy of Mathematics 8​

Answer 1

Answer:

For any polyhedron,

F + V – E = 2

where ‘F’ stands for number of faces, V stands for number of vertices and E stands for number of edges.

This relationship is called Euler’s formula.

Problem: Can a polygon have for its faces:

(i) 3 triangles (ii) 4 triangles (iii) a square and four triangles

Solution:

(i) No, a polyhedron cannot have 3 triangles for its faces.

(ii) Yes, a polyhedron can have four triangles which is known as pyramid on triangular base.