Question

Can a polyhedron have for its faces
(i) 3 triangles?
(ii) 4 triangles?
(iii) A square and four triangles?

Answer 1

Hint: In order to solve this problem use the definition of polyhedron and visualize if it is possible to create a shape with the help of given figures. A solid figure consists of four or more plane faces (all polygons), pairs of which meet along an edge, three or more edges meeting at a vertex.

Complete step-by-step answer:
Polyhedron: A three-dimensional figure whose faces are all polygons. A polyhedron has to have a minimum of four faces.
(i) No, a polyhedron cannot have 3 triangles for its faces. Because a polyhedron must have edge meetings at vertices which are points.
(ii) Yes, a polyhedron can have four triangles which is known as a pyramid on a triangular base. Because all the edges are meeting at the vertices.
(iii) Yes, a polyhedron has its faces a square and four triangles which makes a pyramid on a square base. Because all the eight edges meet at the vertices.
Hence, a polyhedron can be made from 4 triangles and a square and four triangles. But it cannot be made from 3 triangles.
So option (i) is incorrect but (ii) and (iii) are correct.

Note- A polyhedron is a three dimensional shape with flat polygonal faces, straight edges and sharp corners or vertices. A polyhedron with 4 triangles as faces is called a triangular pyramid and one with one square and four triangles is called a square based pyramid.