Question

"Question 1 Can a polyhedron have for its faces (i) 3 triangles? (ii) 4 triangles? (iii) a square and four triangles?

Class 8 Visualising Solid Shapes Page 166"

Answer 1

• Polyhedron: A three-dimensional figure whose faces are all polygons.

Regular polyhedrons: A polyhedron is said to be regular if its faces are made up of regular polygons and the same number of faces meet at each vertex.

 

 

• Prism: A polyhedron whose bottom and top faces (known as bases) are congruent polygons & faces known as lateral faces are parallelograms.

When the side faces are rectangles, the shape is known as right prism.

• Pyramid: A polyhedron whose base is a polygon and lateral faces are triangles

with a common vertex.

A prism or a pyramid is named after its base. Thus a hexagonal prism has a hexagon as its base; and a triangular pyramid has a triangle as its base

Face: A flat surface of a three dimensional figure.

 Edge: Line segment where two faces of solid meet.

• Vertex: A point where three of more edges meet.

• Base: The face that is used to name a polyhedron.

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Solution:

(i)  A polyhedron cannot have 3 triangles for its faces.

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

(iii)  A polyhedron has its faces a square and four triangles which makes a pyramid on square base.

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Hope this will help you...

Answer 2

Answer:

1. No , because polyhendron must have edges meetings at vertices which are points.
2. Yes, because all the edges are meeting at the vertices.
3. Yes , because all the eight edges meet at the vertices.