How many diagonals are there in a decagon?

Answer 1

A decagon has 35 diagonals. A Nonagon has 27 diagonals. An Octagon has 20 diagonals. A Heptagon has 14 diagonals. A Hexagon has 9 diagonals. A Pentagon has 5 Diagonals. A Square has 2 Diagonals. A triangle has 0 Diagonals.

Do you get the point?

0+2+3+4+7+8. Starting with the triangle.

you don't need to start with the triangle because it is 0 diagonals and will not count when you add it up anyways. And don't call it a square, call it a quadrilateral.

Shut up

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-Imagine a hexagone

-There are two vertices at the top which make a horizontal line

- Opposite them there are 2 vertices on the bottom which we can draw straight lines to

therefore

-There would have been 6 connections per point, but we eliminated 3

(n-3)

--

-The connections occur for every vertex in the shape

therefore

n(n-3)

--

We don't want to draw the same connections twice once we get around to vertices on the opposite side of the shape

therefore

n/2(n-3)

where n is the number of faces

This may be applied to many if not all polygons. A Decagon has 36 sides not 35...
There are 35 diagonals in a 10 sided decagon