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AnswerQuestion Answers for Class 12Class 12 BiologyClass 12 ChemistryClass 12 EnglishClass 12 MathsClass 12 PhysicsClass 12 Social ScienceClass 12 Business StudiesClass 12 EconomicsQuestion Answers for Class 11Class 11 EconomicsClass 11 Computer ScienceClass 11 BiologyClass 11 ChemistryClass 11 EnglishClass 11 MathsClass 11 PhysicsClass 11 Social ScienceClass 11 AccountancyClass 11 Business StudiesQuestion Answers for Class 10Class 10 ScienceClass 10 EnglishClass 10 MathsClass 10 Social ScienceClass 10 General KnowledgeQuestion Answers for Class 9Class 9 General KnowledgeClass 9 ScienceClass 9 EnglishClass 9 MathsClass 9 Social ScienceQuestion Answers for Class 8Class 8 ScienceClass 8 EnglishClass 8 MathsClass 8 Social ScienceQuestion Answers for Class 7Class 7 ScienceClass 7 EnglishClass 7 MathsClass 7 Social ScienceQuestion Answers for Class 6Class 6 ScienceClass 6 EnglishClass 6 MathsClass 6 Social ScienceQuestion Answers for Class 5Class 5 ScienceClass 5 EnglishClass 5 MathsClass 5 Social ScienceQuestion Answers for Class 4Class 4 ScienceClass 4 EnglishClass 4 MathsHow many faces, edges and vertices does a pyramid have with n sided polygon as its base?AnswerVerified585.9k+ viewsHint: In this question, we have been asked the number of faces, edges and vertices a pyramid has. To solve this question, we need basic idea about faces, edges and vertices of a three dimensional figure. Let's see the below labelled diagram of cuboid. Observe that the above cuboid has 6 faces, 8 edges and 12 vertices.Similarly, A pyramid is a 3 dimensional figure and the number of edges, faces and vertices depends on the sides of the base.Moreover, we are not given any particular base of the pyramid. We have been asked the general formula with side ‘n’. Complete step-by-step answer:We have been asked the number of faces, edges and vertices of a pyramid whose base is unknown. We have to find a generalized formula in terms of ‘n’. Before finding a generalized formula, let us look at certain pictures of a pyramid with different bases and find their faces, edges and vertices. Using them, we will derive the generalized formula. 1) Faces: (i) Pyramid with 3-sided base: This pyramid has 4 faces. One face which is the base and 3 faces connecting the base with the apex (top most vertex). (ii) Pyramid with 4-sided base: This pyramid has 5 faces. One face as the base and other 4 faces connecting the base with the apex. As we can notice, the total faces are one more than the number of sides of the base. Therefore, a pyramid with ‘n’ sided polygon as base will have $\left( {n + 1} \right)$ faces. 2) Edges:(i) Pyramid with 3-sided base: This pyramid has 6 edges – 3 edges making up the polygon as base and other 3 edges connecting the base to the apex. (ii) Pyramid with 4-sided base: This pyramid has 8 edges – 4 edges making up the polygon as base and other 4 edges connecting the base to the apex. If you will observe, the total edges are twice the number of sides of the base. Therefore, a pyramid with an ‘n’ sided polygon as base will have ($2n$) edges.3) Vertices:(i) Pyramid with 3-sided base: This pyramid has 4 vertices – 3 vertices of the base and 1 apex.(ii) Pyramid with 4-sided base: This pyramid has 5 vertices – 4 vertices of the base and 1 apex. On observation, we can tell that the total vertices are one more than the number of sides of the base. Therefore, a pyramid with ‘n’ sided polygon as base will have $\left( {n + 1} \right)$ vertices.Note: We can observe that a pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form a triangle, called a lateral face. It is a conic solid with a polygonal base. A pyramid is usually assumed to be a regular square pyramid, like the physical pyramid structures. A triangle based pyramid is more often called a tetrahedron.Recently Updated PagesBasicity of sulphurous acid and sulphuric acid areMaster Class 9 Social Science: Engaging Questions & Answers for SuccessMaster Class 9 Science: Engaging Questions & Answers for SuccessMaster Class 9 Maths: Engaging Questions & Answers for SuccessMaster Class 9 General Knowledge: Engaging Questions & Answers for SuccessClass 9 Question and Answer - Your Ultimate Solutions GuideBasicity of sulphurous acid and sulphuric acid areMaster Class 9 Social Science: Engaging Questions & Answers for SuccessMaster Class 9 Science: Engaging Questions & Answers for SuccessMaster Class 9 Maths: Engaging Questions & Answers for SuccessMaster Class 9 General Knowledge: Engaging Questions & Answers for SuccessClass 9 Question and Answer - Your Ultimate Solutions Guide

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