Calculate the maximum number of diagonals that can be drawn in an octagon using the suitable formula.

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answer is A.

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Detailed Solution

Concept- Here, the n-sided polygon given to us is an 8-sided polygon, that is, an octagon. The octagon has eight equal sides. For n-sided polygons, the maximum number of diagonals is calculated using the following combinatorial formula:

, where n is the number of sides or corners.
Now, in an octagon, the number of corners and sides is eight.
Therefore, each vertex has five diagonals connected to the opposite vertex.
For n-sided polygons, the formula for the number of diagonals is given in combination as follows:

, where n is the number of sides or corners. Extending and simplifying this, it looks like this:
Question Image

Here, in the case of an octagon, the number of sides is eight. That is, n is 8. So if you replace it with n = 8,
The maximum number of diagonals that can be drawn is:
Question Image

Hence, the correct answer is option 1) .

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