Question

how many diagonals does a convex polygon have​

Answer 1

Answer:

Math Forum - Ask Dr. Math Archives: Polygon Diagonals. The number of diagonals in a polygon = n(n-3)/2, where n is the number of polygon sides. For a convex n-sided polygon, there are n vertices, and from each vertex you can draw n-3 diagonals, so the total number of diagonals that can be drawn is n(n-3).

Step-by-step explanation:

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Answer 2

A convex polygon with n sides have​ n(n- 3)/2  Diagonals

convex polygon

In a convex polygon, any two interior points can be connected with a  segment completely inside the polygon.

No line containing a side of a convex polygon passes through the inside of that polygon.

convex polygon with  n sides .

2 points are needed to have a diagonal

If one point is selected then another point can not be the same point , or points of two sides from that points.

Hence both points can be selected in n(n - 3) ways

As order of selection of point does not matter

Diagonal AC and CA are same thing

Hence number of diagonals are n(n - 3)/2

Few Examples

Shapes   Number of Sides n        Diagonals n(n-3)/2

Triangle                  3                       0

Quadrilateral           4                      2

Pentagon                 5                      5

Hexagon                  6                      9

a convex polygon with n sides have​ n(n -3)/2  Diagonals

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