To find the diagonals of a seven sided polygon

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by GMATGuruNY » Wed Jan 01, 2014 6:29 am
gmattesttaker2 wrote:Hello,

Can you please assist with this:

In a polygon, a diagonal is defined as the line that joins a vertex to any other vertex except the two adjacent vertices. How many diagonals does a seven-sided polygon have?

OA: 14

Thanks a lot,
Sri
A 7-sided polygon has 7 vertices.
Any combination of 2 NON-ADJACENT vertices can serve to form a diagonal.
From the 7 vertices, the number of combinations of 2 that can be formed = 7C2 = (7*6)/(2*1) = 21.
These 21 combinations include the 7 sides of the polygon.
Subtracting the 7 sides of the polygon from the 21 combinations that can be formed, we get:
21-7 = 14 diagonals.

An alternate approach is to WRITE IT OUT.
Let the 7 vertices be A, B, C, D, E, F and G.
Any non-adacent pair of vertices can serve to form a diagonal.
Options:
AC, AD, AE, AF
BD, BE, BF, BG
CE, CF, CG
DF, DG
EG
Total options = 14.
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by gmattesttaker2 » Wed Jan 01, 2014 7:32 pm
GMATGuruNY wrote:
gmattesttaker2 wrote:Hello,

Can you please assist with this:

In a polygon, a diagonal is defined as the line that joins a vertex to any other vertex except the two adjacent vertices. How many diagonals does a seven-sided polygon have?

OA: 14

Thanks a lot,
Sri
A 7-sided polygon has 7 vertices.
Any combination of 2 NON-ADJACENT vertices can serve to form a diagonal.
From the 7 vertices, the number of combinations of 2 that can be formed = 7C2 = (7*6)/(2*1) = 21.
These 21 combinations include the 7 sides of the polygon.
Subtracting the 7 sides of the polygon from the 21 combinations that can be formed, we get:
21-7 = 14 diagonals.

An alternate approach is to WRITE IT OUT.
Let the 7 vertices be A, B, C, D, E, F and G.
Any non-adacent pair of vertices can serve to form a diagonal.
Options:
AC, AD, AE, AF
BD, BE, BF, BG
CE, CF, CG
DF, DG
EG
Total options = 14.
Hello Mitch,

Thank you very much for your thorough explanation and for the example.

Best Regards,
Sri