Question

HOW MANY DIAGONALS CAN BE DRAWN IN DECAGON

Answer 1

54 Diagonals can be drawn in decagon

Answer 2

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.