Math, asked by shreenidhi3, 1 year ago

HOW MANY DIAGONALS CAN BE DRAWN IN DECAGON

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Answers

Answered by 1KaranBrar
1
54 Diagonals can be drawn in decagon

shreenidhi3: But plz can u solve it using permutations and combination
Answered by fahadahmad1
1
The number of diagonals for a polygon with side 'n' is :
n(n-3)/2
Side in decagon are 10.
(10×7)/2
=35.
Therefore it has 35 diagonals. PROOF Each diagonal connects one point to another point in the polygon that isn’t its next-door neighbor. In an n-sided polygon, you have n starting points for diagonals. And each diagonal can go to (n – 3) ending points because a diagonal can’t end at its own starting point or at either of the two neighboring points. So the first step is to multiply n by (n – 3). Then, because each diagonal’s ending point can be used as a starting point as well, the product n(n – 3) counts each diagonal twice. That’s why you divide by 2.

shreenidhi3: How can it be n(n-3)÷ 2
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