How many diagnals in a pentagon shape?

Answer 1

to make any line you need two points..

so.. a pentagon has 5 vertices - ie. 5 points

so how many ways can you select a combination of 2 - out of 5 points..

1,2,3,4,5

1. (1,2)
2. (1,3 )
3. (1,4 )
4. (1,5 )
5. (2, 3)
6. (2,4 )
7. (2,5 )
8. (3, 4)
9. (3, 5)
10. (4, 5)

so, there you have it -> total of 10 ways :) -> so 10 diagonals.

now of course you could also think like this: ie. pose the question as follows

how many ways can one select r number of goods from P number of total items:

here in YOUR EXAMPLE: R =2 AND P =5

AND well, its a combination of r froma set of p -> which you are looking at:

hence the answer = n c r = factorial n divided by factorial r = 5! / [2! x 3!] =

= (5 X4X3X2X1) / (2x1).(3x2x1) = 5 x 2 = 10

Summarize now: you need a combination of 2 from a total of 5 .. and the formula is => factorial 5 - divided by factorial 3 divided by factorial 2

or mathematically expressed as n C r -> again, in your example, n = 5 [ pentagon] r = 2 [ you are looking for diagonals and it takes two to tango]

[ note: 2,1 is the same as 1,2 and 2,3 is the same as 3,2 and 2,4 is the same as.... etc etc ....]

cheers

olga lednichenko

Answer 2

it has 3 diagnols this is the right answers im sure because a diagonal is when a vertice meets another vertice and they join together and make a shape.