Question

how many diagonals can be drawn for regular pentagon??



answers please?​

Answer 1

Answer:

Diagonals are line segments that connect the vertices of a convex polygon that are not sides. The red lines are all diagonals. This pentagon has 5 diagonals. Whether a polygon is convex or concave, it can always be named by the number of sides.

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Answer 2

Solution :

For a polygon of n sides , the number of diagonals that can be drawn is n(n-3)/2 .

For a pentagon , n = 5 .

Hence , number of diagonals = 5 .

This is the answer .

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Additional Information -

Derivation Of Formula For Number Of Diagonals -

Suppose that there is a polygon which has n sides .

So, this polygon has n vertices .

A diagonal can connect any two non adjacent vertex .

This can be done in n_c_2 ways .

However all the vertices overlap once .

Thus , the number of diagonals become -

→ n_c_2 - n ways

=>[ n! / 2! . ( n - 2 )! ] - n

=> { n(n-1)/2 } - n

=> [ n² - n / 2 ] - n

=> [ n² - 3n ]/2

=> n(n-3)/2 ways .

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