SOLUTION: what is the formula for finding the number of diagonals in a shape e.g. triangle has 0 diagonals, quadrilateral has 2 diagonals, pentagon has 5 diagonals, hexagon has 9 diagonals,
Algebra.Com
Question 549565: what is the formula for finding the number of diagonals in a shape e.g. triangle has 0 diagonals, quadrilateral has 2 diagonals, pentagon has 5 diagonals, hexagon has 9 diagonals, and so on.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
what is the formula for finding the number of diagonals in a shape e.g. triangle has 0 diagonals, quadrilateral has 2 diagonals, pentagon has 5 diagonals, hexagon has 9 diagonals, and so on.
-------
An n-gon has n vertices.
Each pair of vertices determins a line: nC2 = [n(n-1)]/2] lines
-----------
n of those lines are sides of the n-gon
----------------
So, # of diagonals = nC2 - n
----------------------------------
triangle: # = 3C2-n = 3-3 = 0
----------
quadrilater: # = 4C2 - 4 = 6-4 = 2
----------
pentagon: # = 5C2 - 5 = 10-5 = 5
----
etc.
===============
Cheers,
Stan H.
RELATED QUESTIONS
The diagonals of quadrilateral EFGH intersect 0(0, 3) has vertices a parallelogram ? E(1, (answered by ikleyn)
What are the diagonals of a... (answered by 303795)
A quadrilateral has 4 sides and 2 diagonals. A pentagon has 5 sides and 5 diagonals. You... (answered by ikleyn)
the diagonals of quadrilateral efgh intersects at d(1,2) efgh has vertices at e(4,6) and... (answered by greenestamps)
what formula do i use to find the slope of two diagonals in a... (answered by solver91311)
The number of diagonals d in a polygon with n sides is given by the formula d=n^2-3n/2.... (answered by HyperBrain)
what polygon has a number of sides that is five times the number of... (answered by KMST)
The diagonals of quadrilateral ABCD intersect at E(- 1, 4) . ABCD has vertices at A(1, 7) (answered by jim_thompson5910,MathLover1,ikleyn)
This is the problem:
Can you show that no polygon exists in which the ratio of the... (answered by stanbon)