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How Many Diagonals Does Each Of The Following Have?

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How many diagonals does each of the following have?(a) A convex
How many diagonals does each of the following have?(a) A convex from www.toppr.com

In geometry, a diagonal is a line segment that connects two non-adjacent vertices of a polygon. It is important to know the number of diagonals in a polygon, as it can help in solving various problems related to the polygon. In this article, we will discuss the number of diagonals in various polygons.

Number of Diagonals in a Triangle

A triangle is a polygon with three sides and three angles. It is the simplest polygon, and its diagonals can be easily calculated. A triangle has no diagonals, as all its vertices are adjacent to each other.

Number of Diagonals in a Quadrilateral

A quadrilateral is a polygon with four sides and four angles. It is a more complex polygon than a triangle, and its diagonals can be calculated using a formula. The formula to calculate the number of diagonals in a quadrilateral is:

  • Number of Diagonals = (n x (n-3))/2

    • Where n is the number of sides in the quadrilateral. By substituting the value of n as 4, we get:

  • Number of Diagonals = (4 x (4-3))/2 = 2

    • Therefore, a quadrilateral has two diagonals.

    Number of Diagonals in a Pentagon

    A pentagon is a polygon with five sides and five angles. Its diagonals can be calculated using the same formula that we used for a quadrilateral. By substituting the value of n as 5, we get:

  • Number of Diagonals = (5 x (5-3))/2 = 5

    • Therefore, a pentagon has five diagonals.

    Number of Diagonals in a Hexagon

    A hexagon is a polygon with six sides and six angles. Its diagonals can also be calculated using the same formula. By substituting the value of n as 6, we get:

  • Number of Diagonals = (6 x (6-3))/2 = 9

    • Therefore, a hexagon has nine diagonals.

    Number of Diagonals in an Octagon

    An octagon is a polygon with eight sides and eight angles. Its diagonals can be calculated using the same formula. By substituting the value of n as 8, we get:

  • Number of Diagonals = (8 x (8-3))/2 = 20

    • Therefore, an octagon has twenty diagonals.

    Number of Diagonals in a Decagon

    A decagon is a polygon with ten sides and ten angles. Its diagonals can also be calculated using the same formula. By substituting the value of n as 10, we get:

  • Number of Diagonals = (10 x (10-3))/2 = 35

    • Therefore, a decagon has thirty-five diagonals.

    Conclusion

    Knowing the number of diagonals in a polygon can help in solving various problems related to the polygon. In this article, we discussed the number of diagonals in various polygons, including a triangle, quadrilateral, pentagon, hexagon, octagon, and decagon. We used a formula to calculate the number of diagonals in each polygon, and found that the number of diagonals increases with the number of sides in the polygon. Therefore, it is important to have a good understanding of the number of diagonals in polygons, as it can be useful in various fields such as mathematics, engineering, and architecture.

    So, next time you encounter a polygon, remember to calculate its diagonals!

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