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PnC Number of Diagonals in an Octagon - Permutation and Combination, Aptitude Video Lecture - UPSC

FAQs on PnC Number of Diagonals in an Octagon - Permutation and Combination, Aptitude Video Lecture - UPSC

1. How do you find the number of diagonals in an octagon using Permutation and Combination?

Ans. To find the number of diagonals in an octagon using Permutation and Combination, we can apply the formula for combinations. The formula for combinations is given by nC2 = n! / (r! * (n-r)!), where n is the total number of vertices in the polygon and r is the number of vertices required to form a diagonal. In the case of an octagon, there are 8 vertices, so we substitute n = 8 and r = 2 into the formula. 8C2 = 8! / (2! * (8-2)!) = 8! / (2! * 6!) = (8 * 7) / (2 * 1) = 28 Therefore, there are 28 diagonals in an octagon.

2. What is the difference between a diagonal and a side in an octagon?

Ans. In an octagon, a side is a line segment that connects two consecutive vertices of the polygon. It lies entirely within the octagon. On the other hand, a diagonal is a line segment that connects any two non-consecutive vertices of the octagon. It cuts across the interior of the octagon and does not lie entirely within the polygon. In simpler terms, a side is a line segment that forms the boundary of the octagon, while a diagonal is a line segment that crosses the interior of the octagon.

3. Can we count the sides of an octagon as diagonals?

Ans. No, we cannot count the sides of an octagon as diagonals. Diagonals and sides are two distinct concepts in geometry. Sides are line segments that form the boundary of the polygon, while diagonals are line segments that connect non-consecutive vertices of the polygon. In an octagon, there are 8 sides, which are the line segments forming the boundary of the shape. Diagonals, on the other hand, are line segments that cross the interior of the octagon and connect any two non-consecutive vertices. Counting the sides as diagonals would be incorrect and would result in an inaccurate count.

4. Is it necessary to use Permutation and Combination to find the number of diagonals in an octagon?

Ans. No, it is not necessary to use Permutation and Combination to find the number of diagonals in an octagon. While Permutation and Combination can be used to calculate the number of diagonals, there are other methods as well. One alternative method is to use the formula for the number of diagonals in a polygon, which is given by n(n-3)/2, where n is the number of sides/vertices of the polygon. For an octagon, n = 8. Using this formula, we can calculate the number of diagonals in an octagon as 8(8-3)/2 = 8(5)/2 = 40/2 = 20. Therefore, there are 20 diagonals in an octagon.

5. Can the number of diagonals in an octagon be calculated using basic arithmetic operations?

Ans. Yes, the number of diagonals in an octagon can be calculated using basic arithmetic operations. As mentioned earlier, the formula for the number of diagonals in a polygon is given by n(n-3)/2, where n is the number of sides/vertices of the polygon. For an octagon, n = 8. Substituting this value into the formula, we get: 8(8-3)/2 = 8(5)/2 = 40/2 = 20 Therefore, there are 20 diagonals in an octagon. This calculation can be performed using basic arithmetic operations like multiplication and division.

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Oct 03, 2025 Last updated

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