Difficulty: Easy
Correct Answer: 14
Explanation:
Introduction / Context:
This question tests your understanding of how to count the number of diagonals in a polygon using a standard combinatorial formula. Diagonals are line segments that join two non-adjacent vertices of a polygon, and knowing how to compute them quickly is a common aptitude and competitive exam skill.
Given Data / Assumptions:
Concept / Approach:
The total number of straight line segments that can be drawn between n vertices is given by the combination nC2, because each segment is determined by choosing 2 distinct vertices. Among these, n segments are sides of the polygon. The remaining segments are diagonals. There is also a direct formula for diagonals in an n sided polygon: number of diagonals = n * (n - 3) / 2.
Step-by-Step Solution:
Let n = 7 for a 7 sided polygon.Use the diagonal formula: diagonals = n * (n - 3) / 2.Substitute n = 7: diagonals = 7 * (7 - 3) / 2.Compute the expression: 7 * 4 / 2 = 28 / 2.Therefore, number of diagonals = 14.
Verification / Alternative check:
You can also compute total segments: 7C2 = (7 * 6) / 2 = 21.Subtract the 7 sides to get diagonals: 21 - 7 = 14.Both methods give the same result, confirming the answer.
Why Other Options Are Wrong:
7 is just the number of sides, not the number of diagonals.15 is slightly larger than the correct count and could come from careless arithmetic on the formula.21 is the total number of line segments between vertices, including sides, so it overcounts.
Common Pitfalls:
Students sometimes forget to subtract the sides from the total segments.Another common mistake is using n * (n - 1) instead of nC2.Some may misremember the formula as n * (n - 2) / 2, which is incorrect for diagonals.
Final Answer:
The number of diagonals in a 7 sided polygon is 14.
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