Using combinations, determine how many diagonals are in a pentagon and hexagon.
Thanks
2007-07-18 07:50:07 · 3 answers · asked by Icobes 2 in Science & Mathematics ➔ Mathematics
A diagonal connects 2 vertices. There are nC2 ways of choosing the two vertices to be connected. However, n of these will be sides of the figure, so the formula is
nC2-n
Pentagon: 5C2-5=5
Hexagon: 6C2-6=9
2007-07-18 08:16:32 · answer #1 · answered by Anonymous · 0⤊ 0⤋
One diagonal needs 2 peaks
In Pentagon
Comb(5,2)=5!/(2!*3!)=10
Then we must abstract
the 5 sides and we have
finally 5 diagonals
In hexagon
Comb(6,2)=15
minus the 6 sides finally
9 diagonals
2007-07-18 15:13:14 · answer #2 · answered by katsaounisvagelis 5 · 0⤊ 0⤋
Pentagon:
5 * (5-3) / 2 = 5
Hexagon:
6 * (6-2) / 2 = 12
n-tagon:
n * (n-2) / 2
2007-07-18 15:05:04 · answer #3 · answered by oregfiu 7 · 0⤊ 0⤋