Question 14 of 16intermediate🔍 AnalyzeShort Answer2 marks

How did you count them such that you do not miss out any edge or count an edge twice?

Correct Answer

Method 1: Mark each edge as you count it.

Method 2: Count edges face by face and divide by 2 (since each edge belongs to 2 faces).

Method 3: Use the formula: Edges = (Faces × Sides per face) ÷ 2.

Icosahedron: (20×320 \times 3) ÷ 2 = 30 edges.

Dodecahedron: (12×512 \times 5) ÷ 2 = 30 edges.

Exercise: Icosahedron and Dodecahedron | Q: 44 | (Page Page 12)
For More Understanding

Explanation

The chapter encourages systematic counting strategies. Since each edge is shared by exactly 2 faces, counting all sides of all faces and dividing by 2 gives the correct number of edges. This method ensures no edge is missed or counted twice.

Solution Steps

  1. Step 1: Count all sides of all faces.

  2. Step 2: Divide by 2 because each edge belongs to 2 faces.

  3. Step 3: For icosahedron: 20 faces × 3 sides = 60, 60 ÷ 2 = 30 edges.

  4. Step 4: For dodecahedron: 12 faces × 5 sides = 60, 60 ÷ 2 = 30 edges.

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