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The number of diagonal in decagon?
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The number of diagonal in decagon?
Number of Diagonals in a Decagon
A decagon is a polygon with ten sides and ten vertices. To find the number of diagonals in a decagon, we need to understand what a diagonal is first. A diagonal is a line segment that connects two non-adjacent vertices of a polygon. In other words, it is a line that goes from one corner of the polygon to another corner that is not adjacent to it.
Formula for Finding the Number of Diagonals in a Decagon
The formula for finding the number of diagonals in a decagon is:
Number of diagonals = (n(n-3))/2
In this formula, n represents the number of sides of the polygon. For a decagon, n = 10.
Substituting the values in the formula:
Number of diagonals = (10(10-3))/2
Number of diagonals = (10*7)/2
Number of diagonals = 35
Explanation of the Formula
The formula for finding the number of diagonals in a polygon is derived from the fact that each vertex of the polygon can be connected to every other vertex except for the two adjacent vertices. For a polygon with n sides, there are n vertices, and each vertex can be connected to (n-3) other vertices. This is because there are two adjacent vertices, and we cannot connect a diagonal to them. So, the total number of diagonals that can be drawn from a single vertex is (n-3).
However, we need to be careful when counting the diagonals. If we count all the diagonals that can be drawn from each vertex, we will be counting each diagonal twice. For example, the diagonal connecting vertex A to vertex C is the same as the diagonal connecting vertex C to vertex A. Therefore, we need to divide the total number of diagonals by 2 to get the actual number of diagonals in the polygon.
Conclusion
Therefore, the number of diagonals in a decagon is 35. We can use the same formula to find the number of diagonals in any polygon, as long as we know the number of sides of the polygon. Understanding this formula can help us solve many geometry problems involving polygons.
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The number of diagonal in decagon?
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The number of diagonal in decagon? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The number of diagonal in decagon? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of diagonal in decagon?.
The number of diagonal in decagon? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about The number of diagonal in decagon? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The number of diagonal in decagon?.
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