M-Magic 05 || Number of diagonals

The number of diagonals in a convex n-sided regular polygon = n(n-3)/2, where n is the number of polygon sides. 

Q. How many diagonals are drawn in a triangle?

Sol.

Number of sides = 3

then formula = n(n-3)/2

= 3(3-3)/2

= 3(0)/2

= 0

Q. How many diagonals are drawn in a quadrilateral?

Sol.

Number of sides = 4

then formula = n(n-3)/2

= 4(4-3)/2

= 4(1)/2

= 4/2

=2

Q. How many diagonals are drawn in a regular pentagon?

Sol.

Number of sides = 5

then formula = n(n-3)/2

= 5(5-3)/2

= 5(2)/2

= 10/2

= 5

Q. How many diagonals are drawn in a regular hexagon ?

Sol.

Number of sides = 

then formula = n(n-3)/2

= 6(6–3)/2

= 6(3)/2

= 3(3)

= 9

* Now you can find the number of diagonals in any type of the regular polygon by using the formula = n(n-3)/2