Question 12 of 13intermediate🔧 ApplyNumerical4 marks

If the congruent polygons of a prism have 10 sides, how many faces, edges and vertices does the prism have? What if the polygons have nn sides?

Correct Answer

For a prism with 10-sided congruent polygons:

Number of faces: 10 + 2 = 12 (10 rectangular faces + 2 polygonal bases)

Number of edges: 10 + 10 + 10 = 30 (10 edges on each base + 10 edges connecting corresponding vertices)

Number of vertices: 10 + 10 = 20 (10 vertices on each base)

For an n-sided polygon prism: Faces = n + 2 Edges = 3n Vertices = 2n

Exercise: Prisms and Pyramids | Q: 1 | (Page Page 10)
For More Understanding

Explanation

The chapter defines a prism as having two congruent polygons as opposite faces, with edges connecting corresponding vertices. All other faces are parallelograms. The number of faces, edges, and vertices can be derived from the number of sides of the base polygon.

Solution Steps

  1. Step 1: A prism has 2 congruent polygonal bases (faces).

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

  3. Step 3: Total faces = n + 2.

  4. Step 4: Each base has n edges, and there are n edges connecting the bases.

  5. Step 5: Total edges = n + n + n = 3n.

  6. Step 6: Each base has n vertices, so total vertices = 2n.

  7. Step 7: For n = 10: Faces = 12, Edges = 30, Vertices = 20.

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