Question 13 of 13intermediate🔧 ApplyNumerical4 marks

If the base of a pyramid has 10 sides, how many faces, edges and vertices does the pyramid have? What if the base is an nn-sided polygon?

Correct Answer

For a pyramid with 10-sided base: Number of faces = 10 + 1 = 11 (10 triangular faces + 1 polygonal base) Number of edges = 10 + 10 = 20 (10 edges on the base + 10 edges from apex to each vertex) Number of vertices = 10 + 1 = 11 (10 vertices on the base + 1 apex)

For an n-sided base pyramid: Faces = n + 1 Edges = 2n Vertices = n + 1

Exercise: Prisms and Pyramids | Q: 2 | (Page Page 10)
For More Understanding

Explanation

The chapter defines a pyramid as having a polygonal base and a point (apex) outside it, with edges connecting the apex to each vertex of the base. The number of faces, edges, and vertices depends on the number of sides of the base.

Solution Steps

  1. Step 1: A pyramid has 1 polygonal base (face).

  2. Step 2: Number of triangular lateral faces = number of sides of the base = n.

  3. Step 3: Total faces = n + 1.

  4. Step 4: The base has n edges, and there are n edges from apex to base vertices.

  5. Step 5: Total edges = n + n = 2n.

  6. Step 6: The base has n vertices, plus 1 apex vertex.

  7. Step 7: Total vertices = n + 1.

  8. Step 8: For n = 10: Faces = 11, Edges = 20, Vertices = 11.

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