CMA Foundation · Fundamentals of Business Mathematics and Statistics · Permutation and Combinations
How many diagonals does a polygon with 8 sides have?
An octagon has 20 diagonals. Joining any two of the 8 vertices gives 8C2 = 28 lines, and subtracting the 8 sides leaves 20 diagonals. The figure 28 is wrong because it includes the sides of the polygon.
- A20Correct
- B28
- C16
- D8
Explanation
Number of diagonals = nC2 - n = 8C2 - 8 = 28 - 8 = 20. Option 28 counts all lines joining pairs of vertices, including the 8 sides.
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